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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.

There are two types of bordism groups: bordism groups, also called cobordism groups or cobordism rings, and there are singular bordism groups. The bordism groups give a ...

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) ...

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 primitive group action is transitive and it has no nontrivial group blocks. A transitive group action that is not primitive is called imprimitive. A group that has a ...

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

One of the symmetry groups of the Platonic solids. There are three polyhedral groups: the tetrahedral group of order 12, the octahedral group of order 24, and the icosahedral ...