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Every ( nontrivial ) group has a normal series of length 1, namely

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## Some Related Sentences

Every and nontrivial

__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__formally real Jordan algebra can be written as

**a**direct sum

**of**so-called simple ones

**,**which are not themselves direct sums in

**a**

__nontrivial__way.

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 has

__Every__woman

__has__had the experience

**of**saying no when she meant yes

**,**and saying yes when she meant no.

__Every__detail in his interpretation

__has__been beautifully thought out

**,**and

**of**these I would especially cite the delicious laendler touch the pianist brings to the fifth variation

**(**an obvious indication that he is playing with Viennese musicians

**)**

**,**and the gossamer shading throughout.

__Every__family

**of**Riviera Presbyterian Church

__has__been asked to read the Bible and pray together daily during National Christian Family Week and to undertake one project in which all members

**of**the family participate.

__Every__community

**,**if it is alive

__has__

**a**spirit

**,**and that spirit is the center

**of**its unity and identity.

__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.
The restricted principle "

__Every__partially ordered set__has__**a**maximal totally ordered subset " is also equivalent to AC over ZF.
** Tukey's lemma:

__Every__non-empty collection**of**finite character__has__**a**maximal element with respect to inclusion.
*

__Every__continuous functor on**a**small-complete category which satisfies the appropriate solution set condition__has__**a**left-adjoint**(**the Freyd adjoint functor theorem ).__Every__unit

**of**

**length**

__has__

**a**corresponding unit

**of**area

**,**

**namely**the area

**of**

**a**square with the given side

**length**.

__Every__field

__has__an algebraic extension which is algebraically closed

**(**called its algebraic closure ), but proving this in general requires some form

**of**the axiom

**of**choice.

__Every__ATM cell

__has__an 8-or 12-bit Virtual Path Identifier

**(**VPI

**)**and 16-bit Virtual Channel Identifier

**(**VCI

**)**pair defined in its header.

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