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Every proper subgroup of G can be assumed a solvable group, meaning that much theory of such subgroups could be applied.

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## Some Related Sentences

Every and proper

__Every__lattice element

**of**the structure is in its

__proper__place

**,**whether it is

**a**single atom or

**a**molecular grouping

**.**

*

__Every__continuous map from**a**compact space to**a**Hausdorff space is closed and__proper__( i**.**e., the pre-image**of****a**compact set is compact**.**
* In any ring R

**,****a**maximal ideal is an ideal M**that**is maximal in the set**of**all__proper__ideals**of**R**,**i**.**e**.**M is contained in exactly 2 ideals**of**R**,**namely M itself and the entire ring R**.**__Every__maximal ideal is in fact prime**.**__Every__year

**,**thousands

**of**cases

**of**plague are still reported to the World Health Organization

**,**although

**,**with

__proper__treatment

**,**the prognosis for victims is now

**much**better

**.**

__Every__

__proper__rotation is the composition

**of**two reflections

**,**

**a**special case

**of**the Cartan – Dieudonné theorem

**.**

__Every__nontrivial

__proper__rotation in 3 dimensions fixes

**a**unique 1-dimensional linear subspace

**of**R < sup > 3 </ sup > which is called the axis

**of**rotation ( this is Euler's rotation theorem ).

__Every__element in O ( 1

**,**3 )

**can**

**be**written as the semidirect product

**of**

**a**

__proper__

**,**orthochronous transformation and an element

**of**the discrete

**group**

#

__Every__man shall**be**called fairly in turn by the list on board**of**prizes**,**because over and above their__proper__share**,**they are allowed**a**shift**of**clothes**.**__Every__Riemann surface is the quotient

**of**

**a**free

**,**

__proper__and holomorphic action

**of**

**a**discrete

**group**on its universal covering and this universal covering is holomorphically isomorphic ( one also says: " conformally equivalent ") to one

**of**the following:

__Every__elder in the Church is or should

**be**an apostle ;

**that**is

**,**as

**a**minister

**of**the Lord and as

**a**recipient

**of**personal revelation from the Holy Ghost

**,**every elder has the call to bear witness

**of**the truth on all

__proper__occasions

**.**

:

__Every__vessel must at all times maintain**a**__proper__look-out by sight ( day shape or lights by eyes or visual aids ) and hearing ( sound signal or Marine VHF radio ) as well as by all available means ( e**.**g., Radar**,**Automatic Radar Plotting Aid ( ARPA ), Automatic Identification System ( AIS ), GMDSS ...) in order to make**a**full assessment**of**the situation and risk**of**collision**.**__Every__

__proper__coloring and cocoloring

**of**

**a**graph are also subcolorings

**,**so the subchromatic number

**of**any graph is at most equal to the cochromatic number

**,**which is at most equal to the chromatic number

**.**

__Every__infinitesimal region

**of**space time may have its own

__proper__time

**that**corresponds to the gravitational time dilation there

**,**where electromagnetic radiation and matter may

**be**equally affected

**,**since they are made

**of**the same essence ( as shown in many tests involving the famous equation E = mc < sup > 2 </ sup >).

* The embedding theorem for Stein manifolds states the following:

__Every__Stein manifold**of**complex dimension**can****be**embedded into by**a**biholomorphic__proper__map**.**
He summed up his philosophy by saying: "

__Every__Plant has fitness and must**be**placed in its__proper__surroundings so as to bring out its full beauty**.**__Every__living thing was related in

**a**branching pedigree

**,**not ascending

**a**Lamarckian ladder

**,**and this pedigree was the

__proper__basis for classification

**.**

__Every__ornament is at

**a**

__proper__distance

**,**and not one too large

**,**but all delicate and new

**,**with more freedom and variety than Greek ornaments ; and

**,**though probably borrowed from the Hotel de Condé and other new Palaces

**,**not one

**that**is not rather classic than French

**.**

:

__Every__person who under color**of**any statute**,**ordinance**,**regulation**,**custom**,**or usage**,****of**any State or Territory or the District**of**Columbia**,**subjects**,**or causes to**be**subjected**,**any citizen**of**the United States or other person within the jurisdiction thereof to the deprivation**of**any rights**,**privileges**,**or immunities secured by the Constitution and laws**,**shall**be**liable to the party injured in an action at law**,**Suit in equity**,**or other__proper__proceeding for redress**,**except**that**in any action brought against**a**judicial officer for an act or omission taken in**such**officer's judicial capacity**,**injunctive relief shall not**be**granted unless**a**declaratory decree was violated or declaratory relief was unavailable**.**__Every__barangay has

**a**Catholic Chapel

**,**which are maintained by the Lay Ministers Of St

**.**Bartholomew Parish Church-Located in the town

__proper__

**of**San Manuel

**.**

__Every__barangay ( village ) has its own Roman Catholic chapel aside from the parish church in the town

__proper__

**.**

__Every__psyker is in danger

**of**going insane or being possessed by

**a**daemon if he does not have the

__proper__training and strength

**of**will

**.**

Every and subgroup

*

__Every__closed__subgroup__**of****a**profinite**group**is itself profinite ; the topology arising from the profiniteness agrees with the subspace topology**.**
*

__Every__finitely generated**group**with**a**recursively enumerable presentation and insoluble word problem is**a**__subgroup__**of****a**finitely presented**group**with insoluble word problem__Every__

__subgroup__

**of**

**a**topological

**group**is itself

**a**topological

**group**when given the subspace topology

**.**

__Every__open

__subgroup__H is also closed

**,**since the complement

**of**H is the open set given by the union

**of**open sets gH for g in

**G**

__Every__

__subgroup__

**of**

**a**free abelian

**group**is itself free abelian

**,**which is important for the description

**of**

**a**general abelian

**group**as

**a**cokernel

**of**

**a**homomorphism between free abelian groups

**.**

__Every__

**group**

**of**prime order is cyclic

**,**since Lagrange's theorem implies

**that**the cyclic

__subgroup__generated by

Iwasawa worked with so-called-extensions: infinite extensions

**of****a**number field with Galois**group**isomorphic to the additive**group****of**p-adic integers for some prime p**.**__Every__closed__subgroup__**of**is**of**the form**,**so by Galois**theory****,**a-extension is the same thing as**a**tower**of**fields**such****that****.**
*

__Every__triangle**group**T is**a**discrete__subgroup__**of**the isometry**group****of**the sphere ( when T is finite ), the Euclidean plane ( when T has**a**Z + Z__subgroup__**of**finite index ), or the hyperbolic plane**.**
Recall

**that****a**subsemigroup**G****of****a**semigroup S is**a**__subgroup__**of**S ( also called sometimes**a****group**in S ) if there exists an idempotent e**such****that****G**is**a****group**with identity element e**.**A semigroup S is group-bound if some power**of**each element**of**S lies in some__subgroup__**of**S**.**__Every__finite semigroup is group-bound**,**but**a**group-bound semigroup might**be**infinite**.**__Every__

__subgroup__is organized around

**a**set

**of**brothers

**,**each

**of**whom is often married to

**a**

**group**

**of**sisters

**.**

__Every__finite

**group**is

**a**

__subgroup__

**of**the mapping class

**group**

**of**

**a**closed

**,**orientable surface

**,**moreover one

**can**realize any finite

**group**as the

**group**

**of**isometries

**of**some compact Riemann surface

**.**

__Every__quasinormal

__subgroup__is

**a**modular

__subgroup__

**,**

**that**is

**,**

**a**modular element in the lattice

**of**

**subgroups**

**.**

__Every__

**group**has itself ( the improper

__subgroup__) and the trivial

__subgroup__as two

**of**its fully characteristic

**subgroups**

**.**

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