presentation,
n. (Group theory) a set, X, of generators together with a set, R, of relations, such that the group generated by X subject to the relations of R is isomorphic to a given group; a presentation of a group is usually denoted 〈X, R〉. For example,
〈 a, b; a2 = bn = (ab)2 = 1 〉
is a presentation of the dihedral group of degree n, for n ≥ 3. Formally, for R a subset of the free group on X, 〈X, R〉 is a presentation of G if and only if G is isomorphic to the free group on X factored by the normal closure of R in the free group.
〈 a, b; a2 = bn = (ab)2 = 1 〉
is a presentation of the dihedral group of degree n, for n ≥ 3. Formally, for R a subset of the free group on X, 〈X, R〉 is a presentation of G if and only if G is isomorphic to the free group on X factored by the normal closure of R in the free group.