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Conversely if a Kleinian group has no nontrivial torsion elements then it is the fundamental group of a hyperbolic 3-manifold.

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## Some Related Sentences

Conversely and if

__Conversely__,

__if__statistics were uncovered which contradicted

**a**cherished theory,

**the**sources were denounced as faulty

**.**

__Conversely__, experimenters would consider as impressive such statements as

**the**following, which,

__if__they turned out to be hits, are so unusual as to be really significant:

__Conversely__,

__if__he gives

**a**heavy rating to his own reading, and finds more accurate facts in

**it**than in

**the**others,

**a**point

**is**chalked up for

**the**intrinsic, objective meaningfulness

**of**this type

**of**mediumistic material

**.**

__Conversely__,

**a**subset R defines

**a**binary function

__if__and only

__if__, for any x in X and y in Y, there exists

**a**unique z in Z such that ( x, y, z ) belongs to R

**.**

__Conversely__,

__if__

**a**Boolean ring A

**is**given, we can turn

**it**into

**a**Boolean algebra by defining x ∨ y := x + y + ( x · y ) and x ∧ y := x · y

**.**

__Conversely__,

__if__

**the**second theory

**is**correct,

**then**

**the**Athenians were merely reacting to

**the**Persians attacking them

**.**

__Conversely__

**the**equilibrium position

**is**said to be " far to

**the**left "

__if__hardly any product

**is**formed from

**the**reactants

**.**

__Conversely__,

__if__ƒ: C → C

**is**

**a**function which

**is**differentiable when regarded as

**a**function on R < sup > 2 </ sup >,

**then**ƒ

**is**complex differentiable

__if__and only

__if__

**the**Cauchy – Riemann equations hold

**.**

__Conversely__,

__if__

**the**amount

**of**fat

**is**increased, increasing

**the**number

**of**calories ingested will only add weight

**.**

__Conversely__,

__if__

**the**source

**of**waves

**is**moving away from

**the**observer, each wave

**is**emitted from

**a**position farther from

**the**observer than

**the**previous wave, so

**the**arrival time between successive waves

**is**increased, reducing

**the**frequency

**.**

__Conversely__every partition

**of**comes from an equivalence relation in this way, according to which

__if__and only

__if__and belong to

**the**same set

**of**

**the**partition

**.**

If neither A nor B includes

**the**idea**of**existence,**then**" some A are B " simply adjoins A to B**.**__Conversely__,__if__A or B do include**the**idea**of**existence in**the**way that " triangle " contains**the**idea " three angles equal to two right angles ",**then**" A exists "**is**automatically true, and we have an ontological proof**of**A's existence**.**__Conversely__,

__if__

**the**measured potential

**is**negative,

**the**electrode

**is**more oxidizing than

**the**SHE ( such as Zn in ZnSO < sub > 4 </ sub > where

**the**standard electrode potential

**is**− 0

**.**76 V ).

__Conversely__,

__if__

**the**firm

**is**able to get bulk discounts

**of**an input,

**then**

**it**could have economies

**of**scale in some range

**of**output levels even

__if__

**it**

**has**decreasing returns in production in that output range

**.**

__Conversely__, daylight stock shot in daylight will look normal, but orange

__if__shot under tungsten lights

**.**

__Conversely__,

__if__

**the**data are sparse — that

**is**,

__if__only K out

**of**N Fourier coefficients are nonzero —

**then**

**the**complexity can be reduced to O ( K log N log ( N / K )), and this

**has**been demonstrated to lead to practical speedups compared to an ordinary FFT for N / K > 32 in

**a**large-N example ( N = 2 < sup > 22 </ sup >) using

**a**probabilistic approximate algorithm ( which estimates

**the**largest K coefficients to several decimal places ).

Conversely and group

__Conversely__,

**if**( A, m, e, inv )

**is**

**a**

__group__object in one

**of**those categories,

**then**m necessarily coincides with

**the**given operation on A, e

**is**

**the**inclusion

**of**

**the**given identity element on A, inv

**is**

**the**inversion operation and A with

**the**given operation

**is**an abelian

__group__

**.**

__Conversely__, discretionary behavior

**is**motivated by internal values and

**is**seen as more cooperative and therefore ideal within

**a**

__group__

**.**

__Conversely__, other British acts such as Wang Chung, Breathe and Murray Head, as well as

**the**Anglo-Australian duo Air Supply, are one-hit wonders in

**the**UK but not in

**the**US, and

**the**American

__group__3T, best known in their homeland as being

**the**three sons

**of**Tito Jackson

**of**The Jackson 5, along with other bands such as Blind Melon and Deep Blue Something, are one-hit wonders in

**the**US but not in

**the**UK

**.**

__Conversely__,

**a**

__group__may also devolve to an earlier stage

**if**unable to resolve outstanding issues in

**a**particular stage

**.**

__Conversely__,

**it**

**is**

**a**consequence

**of**

**the**subsequent conclusions

**of**

**the**theorem that any compact Lie

__group__

**is**isomorphic to

**a**matrix

__group__

**.**

__Conversely__, any affine linear transformation extends uniquely to

**a**projective linear transformations, so

**the**affine

__group__

**is**

**a**subgroup

**of**

**the**projective

__group__

**.**

__Conversely__,

**if**n

**is**prime,

**then**there exists

**a**primitive root modulo n, or generator

**of**

**the**

__group__( Z / nZ )*.

*

__Conversely__,**a**letter or__group__**of**letters can correspond to different phonemes in different contexts ( as th does in English ; originally this stood for**a**single phoneme, which**then**split ).
Given

**then****a**normal extension L**of**K, with automorphism__group__Aut ( L / K ) = G, and containing α, any element g ( α ) for g in G will be**a**conjugate**of**α, since**the**automorphism g sends roots**of**p to roots**of**p**.**__Conversely__any conjugate β**of**α**is****of**this form: in other words, G acts transitively on**the**conjugates**.**__Conversely__, given

**a**Hopf algebra whose coalgebra structure

**is**given above, we can recover

**a**formal

__group__law F from

**it**

**.**

__Conversely__, given

**a**left kG module M,

**then**M

**is**

**a**k vector space, and multiplication with an element g

**of**G yields

**a**k-linear automorphism

**of**M ( since g

**is**invertible in kG ), which describes

**a**

__group__homomorphism G → GL ( M ).

__Conversely__, Austereo's Triple M

__group__

**of**stations have suffered heavily from increased competition from new station Vega 95

**.**3 and Vega 91

**.**5 in Sydney and Melbourne respectively, with

**the**stations in Melbourne and Sydney recording some

**of**their lowest ratings

**of**all time

**.**

__Conversely__,

**if**one pottery-type suddenly replaces

**a**great diversity

**of**pottery types in an entire region this might be interpreted as

**a**new

__group__migrating in with this new style

**.**

__Conversely__,

**if**

**the**holonomy

__group__

**of**

**the**Riemannian manifold M

**is**contained in Sp ( k ), choose complex structures I < sub > x </ sub >, J < sub > x </ sub > and K < sub > x </ sub > on T < sub > x </ sub > M which make T < sub > x </ sub > M into

**a**quaternionic vector space

**.**

__Conversely__, symmetric tensors are defined as invariants: given

**the**natural action

**of**

**the**symmetric

__group__on

**the**tensor algebra,

**the**symmetric tensors are

**the**subspace on which

**the**symmetric

__group__acts trivially

**.**

__Conversely__,

**if**G contains

**a**proper non-trivial normal subgroup N,

**then**

**the**composition

**of**

**the**natural surjective

__group__homomorphism G → G / N with

**the**regular representation

**of**G / N produces

**a**representation π

**of**G which

**has**kernel N

**.**Taking χ to be

**the**character

**of**some non-trivial subrepresentation

**of**π, we have

**a**character satisfying

**the**hypothesis in

**the**direct statement above

**.**

__Conversely__,

**the**conservative

__group__Americans for Constitutional Action stated Mathias agreed with their positions only 16 %

**of**

**the**time

**.**

To summarize, M

**is****a**symmetric space G / K with**a**compact isotropy__group__K**.**__Conversely__, symmetric spaces with compact isotropy__group__are Riemannian symmetric spaces, although not necessarily in**a**unique way**.**

Conversely and has

__Conversely__, some

**elements**do not maintain distinct allotropes in different phases – for example phosphorus

__has__numerous solid allotropes, which all revert to

**the**same P < sub > 4 </ sub > form when melted to

**the**liquid state

**.**

__Conversely__,

**a**standard line on which voice service

__has__been unsubscribed ( such as an ADSL dry loop ) may still accept calls to

**the**958 test exchange but not allow calls to standard numbers

**.**

__Conversely__,

**the**Belgian Blue's meat tenderness

__has__been argued to be just as tender because there are

**a**large number

**of**smaller muscle fibers

**.**

__Conversely__,

**the**defensive team will know that

**the**offense

__has__to cover

**a**good deal

**of**ground in

**a**single play, will expect

**a**forward pass, and will know from earlier study something

**of**

**the**propensities

**of**

**the**offense they face

**.**

__Conversely__, Clausewitz

__has__also been seen as " The preeminent military and political strategist

**of**limited war in modern times

**.**

__Conversely__,

**if**

**the**odds

**of**drawing

**a**winning card are numerically lower than

**the**pot odds,

**the**call

__has__

**a**negative expectation, and you can expect to win less money on average than

**it**costs to call

**the**bet

**.**

__Conversely__, every preorder

**is**

**the**reachability relationship

**of**

**a**directed graph ( for instance,

**the**graph that

__has__an edge from x to y for every pair ( x, y ) with x ≤ y ).

__Conversely__, in

**the**bleak Orwellian world

**of**" The High Ones "— where

**the**Soviets have won

**the**Third World War and gained control

**of**

**the**whole world —

**the**dissidents still have some hope, precisely because space flight

__has__not been abandoned

**.**

__Conversely__,

**the**interior

**of**

**the**box

__has__

**a**constant, zero potential energy .< ref > Actually, any constant, finite potential can be specified within

**the**box

**.**

__Conversely__, Baptists are underrepresented,

**a**reflection

**of**their quite recent expansion in numbers ; there

__has__been only one Roman Catholic president, although they are currently

**the**largest single denomination, and there have been

**no**Lutheran, Pentecostal, or Latter Day Saint presidents

**.**

__Conversely__, birds

**of**prey-which show distinct reverse sexual dimorphism — tend to be monogamous for long periods or mate for life ; some species like

**the**Snail kite will choose new mates every year, polygyny

**is**noted in many Harriers and polyandry

__has__been observed in

**the**Harris ' Hawk ( notable for being

**the**only bird

**of**prey to regularly live and hunt in family and social groups ) and

**the**aforementioned Galapagos hawk

**.**

__Conversely__, ska and reggae, popular among traditionalist skinheads,

__has__influenced several punk musicians

**.**

__Conversely__, once

**the**hardware and software for an anti-lock braking system

__has__been designed to meet its required deadlines,

**no**further performance gains are obligatory

**.**

__Conversely__,

**the**southern part

__has__tended to sink to compensate, causing flooding

**of**

**the**Low Countries and Denmark

**.**

__Conversely__, Slam poetry movement founder Marc Smith

__has__been critical

**of**

**the**commercially successful Def Poetry television and Broadway live stage shows produced by Russell Simmons, decrying

**it**as " an exploitive entertainment that diminished

**the**value and aesthetic

**of**performance poetry ".

__Conversely__,

**the**Court

__has__approved routine warrantless seizures, for example " where there

**is**probable cause to believe that

**a**criminal offense

__has__been or

**is**being committed

**.**

__Conversely__, Sinhalese

__has__also borrowed from

**the**original Vedda language, words and grammatical structures, differentiating

**it**from its related Indo-Aryan languages

**.**

__Conversely__, Elijah Delmedigo ( c

**.**1458 – c

**.**1493 ), in his Bechinat ha-Dat endeavored to show that

**the**Zohar could not be attributed to Shimon bar Yochai, arguing that

**if**

**it**were his work,

**the**Zohar would have been mentioned by

**the**Talmud, as

__has__been

**the**case with other works

**of**

**the**Talmudic period, that had bar Yochai known by divine revelation

**the**hidden meaning

**of**

**the**precepts, his decisions on Jewish law from

**the**Talmudic period would have been adopted by

**the**Talmud, that

**it**would not contain

**the**names

**of**rabbis who lived at

**a**later period than that

**of**Simeon ; and that

**if**

**the**Kabbalah was

**a**revealed doctrine, there would have been

**no**divergence

**of**opinion among

**the**Kabbalists concerning

**the**mystic interpretation

**of**

**the**precepts

**.**

__Conversely__,

**if**M

**is**positive definite,

**it**

__has__an eigendecomposition P < sup >− 1 </ sup > DP where P

**is**unitary, D diagonal, and all diagonal

**elements**

**of**D are real and positive

**.**

As stated earlier, an adjunction between categories C and D gives rise to

**a**family**of**universal morphisms, one for each object in C and one for each object in D**.**__Conversely__,**if**there exists**a**universal morphism to**a**functor G: C → D from every object**of**D,**then**G__has__**a**left adjoint**.**0.166 seconds.