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Every element in the group can be written as a product of generators, and the growth rate counts the number of elements that can be written as a product of length n.

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## Some Related Sentences

Every and element

__Every__such subset has

**a**smallest

__element__

**,**so to specify our choice function we

**can**simply say

**that**it maps each set to

**the**least

__element__

**of**

**that**set

**.**

** Zorn's lemma:

__Every__non-empty partially ordered set**in**which every chain ( i**.**e**.**totally ordered subset ) has an upper bound contains at least one maximal__element__**.**
** Tukey's lemma:

__Every__non-empty collection**of**finite character has**a**maximal__element__with respect to inclusion**.**__Every__lattice

__element__

**of**

**the**structure is

**in**its proper place

**,**whether it is

**a**single atom or

**a**molecular grouping

**.**

__Every__Boolean algebra ( A

**,**∧, ∨) gives rise to

**a**ring ( A

**,**+, ·) by defining

**a**+ b := (

**a**∧ ¬ b ) ∨ ( b ∧ ¬

**a**) = (

**a**∨ b ) ∧ ¬(

**a**∧ b ) ( this operation is called symmetric difference

**in**

**the**case

**of**sets

**and**XOR

**in**

**the**case

**of**logic )

**and**

**a**· b :=

**a**∧ b

**.**The zero

__element__

**of**this ring coincides with

**the**0

**of**

**the**Boolean algebra ;

**the**multiplicative identity

__element__

**of**

**the**ring is

**the**1

**of**

**the**Boolean algebra

**.**

__Every__repetition

**of**insertion sort removes an

__element__from

**the**input data

**,**inserting it into

**the**correct position

**in**

**the**already-sorted list

**,**until no input

**elements**remain

**.**

__Every__singleton is

**a**terminal object

**,**with

**the**functions mapping all

**elements**

**of**

**the**source sets to

**the**single target

__element__

**as**morphisms

**.**

__Every__

__element__s

**,**except

**a**possible greatest

__element__

**,**has

**a**unique successor ( next

__element__), namely

**the**least

__element__

**of**

**the**subset

**of**all

**elements**greater than s

**.**

__Every__subset which has an upper bound has

**a**least upper bound

**.**

*

__Every__non-empty set**of**left ideals**of**R**,**partially ordered by inclusion**,**has**a**maximal__element__with respect to set inclusion**.**__Every__time

**a**pixel on

**a**triangle is rendered

**,**

**the**corresponding texel ( or texture

__element__)

**in**

**the**texture must

**be**found

**.**

__Every__non-inner automorphism yields

**a**non-trivial

__element__

**of**Out ( G ), but different non-inner automorphisms may yield

**the**same

__element__

**of**Out ( G ).

Every and group

Group actions / representations:

__Every____group__G**can****be**considered**as****a**category with**a**single object whose morphisms are**the****elements****of**G**.**A functor from G to Set is then nothing but**a**__group__action**of**G on**a**particular set**,**i**.**e**.****a**G-set**.**__Every__galaxy

**of**sufficient mass

**in**

**the**Local Group has an associated

__group__

**of**globular clusters

**,**

**and**almost every large galaxy surveyed has been found to possess

**a**system

**of**globular clusters

**.**

*

__Every__Lie__group__is parallelizable**,****and**hence an orientable manifold ( there is**a**bundle isomorphism between its tangent bundle**and****the****product****of**itself with**the**tangent space at**the**identity )__Every__instrumental

__group__( or section ) has

**a**principal who is generally responsible for leading

**the**

__group__

**and**playing orchestral solos

**.**

*

__Every__closed subgroup**of****a**profinite__group__is itself profinite ;**the**topology arising from**the**profiniteness agrees with**the**subspace topology**.**
While he admits

**the**existence**of**caste-based discrimination**,**he writes**that**"__Every__social__group__cannot**be**regarded**as****a**race simply because we want to protect it against prejudice**and**discrimination ".__Every__summer

**the**

__group__gathers

**in**Newport

**,**RI for week long dance training

**,**seaside teas

**,**

**and**evenings enjoying

**the**splendors

**of**

**the**Gilded Age

**.**

*

__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__synset contains

**a**

__group__

**of**synonymous words or collocations (

**a**collocation is

**a**sequence

**of**words

**that**go together to form

**a**specific meaning

**,**such

**as**" car pool "); different senses

**of**

**a**word are

**in**different synsets

**.**

__Every__

__group__

**can**

**be**trivially made into

**a**topological

__group__by considering it with

**the**discrete topology ; such groups are called discrete groups

**.**

__Every__topological

__group__

**can**

**be**viewed

**as**

**a**uniform space

**in**two ways ;

**the**left uniformity turns all left multiplications into uniformly continuous maps while

**the**right uniformity turns all right multiplications into uniformly continuous maps

**.**

__Every__subgroup

**of**

**a**topological

__group__is itself

**a**topological

__group__when given

**the**subspace topology

**.**

__Every__ten years

**,**when

**the**general census

**of**population takes place

**,**each citizen has to declare which linguistic

__group__they belong or want to

**be**aggregated to

**.**

Every and can

__Every__information exchange between living organisms — i

**.**e

**.**transmission

**of**signals

**that**involve

**a**living sender

**and**receiver

__can__

**be**considered

**a**form

**of**communication ;

**and**even primitive creatures such

**as**corals are competent to communicate

**.**

__Every__context-sensitive grammar which does not generate

**the**empty string

__can__

**be**transformed into an equivalent one

**in**Kuroda normal form

**.**

__Every__grammar

**in**Chomsky normal form is context-free

**,**

**and**conversely

**,**every context-free grammar

__can__

**be**transformed into an equivalent one which is

**in**Chomsky normal form

**.**

__Every__module over

**a**division ring has

**a**basis ; linear maps between finite-dimensional modules over

**a**division ring

__can__

**be**described by matrices

**,**

**and**

**the**Gaussian elimination algorithm remains applicable

**.**

__Every__entire function

__can__

**be**represented

**as**

**a**power series

**that**converges uniformly on compact sets

**.**

__Every__sequence

__can__

**,**thus

**,**

**be**read

**in**three reading frames

**,**each

**of**which will produce

**a**different amino acid sequence (

**in**

**the**given example

**,**Gly-Lys-Pro

**,**Gly-Asn

**,**or Glu-Thr

**,**respectively ).

__Every__hyperbola is congruent to

**the**origin-centered East-West opening hyperbola sharing its same eccentricity ε ( its shape

**,**or degree

**of**" spread "),

**and**is also congruent to

**the**origin-centered North-South opening hyperbola with identical eccentricity ε —

**that**is

**,**it

__can__

**be**rotated so

**that**it opens

**in**

**the**desired direction

**and**

__can__

**be**translated ( rigidly moved

**in**

**the**plane ) so

**that**it is centered at

**the**origin

**.**

__Every__holomorphic function

__can__

**be**separated into its real

**and**imaginary parts

**,**

**and**each

**of**these is

**a**solution

**of**Laplace's equation on R < sup > 2 </ sup >.

__Every__species

__can__

**be**given

**a**unique (

**and**

**,**one hopes

**,**stable ) name

**,**

**as**compared with common names

**that**are often neither unique nor consistent from place to place

**and**language to language

**.**

__Every__vector v

**in**determines

**a**linear map from R to taking 1 to v

**,**which

__can__

**be**thought

**of**

**as**

**a**Lie algebra homomorphism

**.**

__Every__use

**of**modus tollens

__can__

**be**converted to

**a**use

**of**modus ponens

**and**one use

**of**transposition to

**the**premise which is

**a**material implication

**.**

__Every__adult

**,**healthy

**,**sane Muslim who has

**the**financial

**and**physical capacity to travel to Mecca

**and**

__can__make arrangements for

**the**care

**of**his / her dependants during

**the**trip

**,**must perform

**the**Hajj once

**in**

**a**lifetime

**.**

*

__Every__finite topological space gives rise to**a**preorder on its points**,****in**which x ≤ y if**and**only if x belongs to every neighborhood**of**y**,****and**every finite preorder__can__**be**formed**as****the**specialization preorder**of****a**topological space**in**this way**.**
*

__Every__preorder__can__**be**given**a**topology**,****the**Alexandrov topology ;**and**indeed**,**every preorder on**a**set is**in**one-to-one correspondence with an Alexandrov topology on**that**set**.**__Every__binary relation R on

**a**set S

__can__

**be**extended to

**a**preorder on S by taking

**the**transitive closure

**and**reflexive closure

**,**R < sup >+=</ sup >.

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