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The singleton set {0}, with respect to the trivial group structure defined by the addition 0+0=0. The element 0 is the additive identity element of the group, and also the ...

The Ree group R(q) is the automorphism group of a S(2,q+1,q^3+1) Steiner system.

The free part of the homology group with a domain of coefficients in the group of integers (if this homology group is finitely generated).

The center of a group is the set of elements which commute with every element of the group. It is equal to the intersection of the centralizers of the group elements.

The unitary group U_n(q) is the set of n×n unitary matrices.

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

Transitivity is a result of the symmetry in the group. A group G is called transitive if its group action (understood to be a subgroup of a permutation group on a set Omega) ...

The group direct sum of a sequence {G_n}_(n=0)^infty of groups G_n is the set of all sequences {g_n}_(n=0)^infty, where each g_n is an element of G_n, and g_n is equal to the ...

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.