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An extension of a group H by a group N is a group G with a normal subgroup M such that M=N and G/M=H. This information can be encoded into a short exact sequence of groups ...

A nilpotent Lie group is a Lie group G which is connected and whose Lie algebra is a nilpotent Lie algebra g. That is, its Lie algebra lower central series ...

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

The projective special unitary group PSU_n(q) is the group obtained from the special unitary group SU_n(q) on factoring by the scalar matrices contained in that group. ...

C_6 is one of the two groups of group order 6 which, unlike D_3, is Abelian. It is also a cyclic. It is isomorphic to C_2×C_3. Examples include the point groups C_6 and S_6, ...

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 ...