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The homeomorphism group of a topological space X is the set of all homeomorphisms f:X->X, which forms a group by composition.

A group G such that the quotient group G/Z(G), where Z(G) is the group center of G, is Abelian. An equivalent condition is that the commutator subgroup G^' is contained in ...

A permutation group in which the permutations are limited to transpositions.

A group having continuous group operations. A continuous group is necessarily infinite, since an infinite group just has to contain an infinite number of elements. But some ...

The Poincaré group is another name for the inhomogeneous Lorentz group (Weinberg 1972, p. 28) and corresponds to the group of inhomogeneous Lorentz transformations, also ...

The trivial group, denoted E or <e>, sometimes also called the identity group, is the unique (up to isomorphism) group containing exactly one element e, the identity element. ...

Rubik's group is the group corresponding to possible rotations of a Rubik's Cube. There are six possible rotations, each corresponding to a generator of the group, and the ...

An alternating group is a group of even permutations on a set of length n, denoted A_n or Alt(n) (Scott 1987, p. 267). Alternating groups are therefore permutation groups. ...

A group which is related to the Taniyama-Shimura conjecture.

The number of elements in a group G, denoted |G|. If the order of a group is a finite number, the group is said to be a finite group. The order of an element g of a finite ...