## Finite Group

In mathematics and abstract algebra, a **finite group** is a group whose underlying set *G* has finitely many elements. During the twentieth century, mathematicians investigated certain aspects of the theory of finite groups in great depth, especially the local theory of finite groups, and the theory of solvable groups and nilpotent groups. A complete determination of the structure of all finite groups is too much to hope for; the number of possible structures soon becomes overwhelming. However, the complete classification of the finite simple groups was achieved, meaning that the "building blocks" from which all finite groups can be built are now known, as each finite group has a composition series.

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### Some articles on finite group:

... to classify projective representations of a

**group**, and the modern formulation of his definition is the second cohomology

**group**H2(G, C×) ... A projective representation is much like a

**group**representation except that instead of a homomorphism into the general linear

**group**GL(n, C), one takes a homomorphism into ... Schur (1904, 1907) showed that every

**finite group**G has associated to it at least one

**finite group**C, called a Schur cover, with the property that every projective representation of G can be ...

... One of the approaches to representations of

**finite groups**is through module theory ... Representations of a

**group**G are replaced by modules over its

**group**algebra K ... Maschke's theorem addresses the question is a general (

**finite**-dimensional) representation built from irreducible subrepresentations using the direct sum operation? In the ...

... In mathematics a

**group**is sometimes called an Iwasawa

**group**or M-

**group**or modular

**group**if its lattice of subgroups is modular ...

**Finite**modular

**groups**are also called Iwasawa

**groups**, after (Iwasawa 1941) where they were classified ... Both

**finite**and infinite M-

**groups**are presented in textbook form in (Schmidt 1994, Ch ...

... Every

**finite group**, by an elementary counting argument ... More generally, every polycyclic-by-

**finite group**... Any finitely-generated free

**group**...

**Finite Group**- Number of Groups of A Given Order - Table of Distinct Groups of Order

*n*

... Order n #

**Groups**Abelian Non-Abelian 0. 18 ...

### Famous quotes containing the words group and/or finite:

“A little *group* of wilful men reflecting no opinion but their own have rendered the great Government of the United States helpless and contemptible.”

—Woodrow Wilson (1856–1924)

“God is a being of transcendent and unlimited perfections: his nature therefore is incomprehensible to *finite* spirits.”

—George Berkeley (1685–1753)