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Every finite simple group is isomorphic to one of the following groups:

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## Some Related Sentences

Every and finite

** Tukey's lemma

**:**__Every__non-empty collection**of**__finite__character has a maximal element with respect**to**inclusion.
Hilbert's example

**:**"**the**assertion that either there are only finitely many prime numbers or there are infinitely many " ( quoted in Davis 2000**:**97 ); and Brouwer's**:**"__Every__mathematical species**is**either__finite__or infinite.
*

__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__rational number / has two closely related expressions as a

__finite__continued fraction, whose coefficients can be determined by applying

**the**Euclidean algorithm

**to**.

__Every__

__finite__

**group**

**of**exponent n with m generators

**is**a homomorphic image

**of**B < sub > 0 </ sub >( m, n ).

__Every__known Sierpinski number k has a small covering set, a

__finite__set

**of**primes with at least

**one**dividing k · 2 < sup > n </ sup >+ 1 for each n > 0.

__Every__finite-dimensional Hausdorff topological vector space

**is**reflexive, because J

**is**bijective by linear algebra, and because there

**is**a unique Hausdorff vector space topology on a

__finite__dimensional vector space.

**:**

__Every__oriented prime closed 3-manifold can be cut along tori, so that

**the**interior

**of**each

**of**

**the**resulting manifolds has a geometric structure with

__finite__volume.

__Every__

__finite__or bounded interval

**of**

**the**real numbers that contains an infinite number

**of**points must have at least

**one**point

**of**accumulation.

__Every__field

**of**either type can be realized as

**the**field

**of**fractions

**of**a Dedekind domain in which every non-zero ideal

**is**

**of**

__finite__index.

__Every__process involving charged particles emits infinitely many coherent photons

**of**infinite wavelength, and

**the**amplitude for emitting any

__finite__number

**of**photons

**is**zero.

*

__Every__finite-dimensional central**simple**algebra over a__finite__field must be a matrix ring over that field.

Every and simple

#

__Every____simple__path from a given node**to**any**of**its descendant leaves contains**the**same number**of**black nodes.__Every__

__simple__R-module

**is**

**isomorphic**

**to**a quotient R / m where m

**is**a maximal right ideal

**of**R. By

**the**above paragraph, any quotient R / m

**is**a

__simple__module.

" I might easily have written this story in

**the**traditional manner [...]__Every__novelist knows**the**recipe [...] It**is**not very difficult**to**follow a__simple__, chronological scheme which**the**critics will understand [...] But I, after all, am trying**to**tell**the**story**of**this Chapelizod family in a new way.__Every__October, Moriarty plays host

**to**

**the**Pinto Bean Fiesta, which

**is**composed

**of**a bunch

**of**

__simple__games in Crossly Park, as well as a parade and crowning

**of**a " Pinto Bean Queen.

__Every__

**one**

**of**

**the**infinitely many vertices

**of**G can be reached from v < sub > 1 </ sub > with a

__simple__path, and each such path must start with

**one**

**of**

**the**finitely many vertices adjacent

**to**v < sub > 1 </ sub >.

__Every__hour that Napoleon could have attacked earlier as he did, would have been

**is**his favour, but

**the**French could not attack in

**the**morning for

**the**

__simple__reason that

**the**entire army had not yet taken its battle positions.

__Every__closed curve c on X

**is**homologous

**to**for some

__simple__closed curves c < sub > i </ sub >, that

**is**,

*

__Every__finite-dimensional__simple__algebra over R must be a matrix ring over R, C, or H.__Every__central__simple__algebra over R must be a matrix ring over R or H. These results follow from**the**Frobenius theorem.
*

__Every__finite-dimensional__simple__algebra over C must be a matrix ring over C and hence every central__simple__algebra over C must be a matrix ring over C.
*

__Every__automorphism**of**a central__simple__algebra**is**an inner automorphism ( follows from Skolem – Noether theorem ).
*

__Every__4-dimensional central__simple__algebra over a field F**is****isomorphic****to**a quaternion algebra ; in fact, it**is**either a two-by-two matrix algebra, or a division algebra.
# Personal right

**:**__Every__person has a right**to**life but this right**is**restricted and has attached certain duties –__simple__living**is**essential.__Every__Sámi settlement had its seita, which had no regular shape, and might consist

**of**smooth or odd-looking stones picked out

**of**a stream,

**of**a small pile

**of**stones,

**of**a tree-stump, or

**of**a

__simple__post.

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