Groups of Finite Weight
Copyright policy )Groups of Finite Weight
If N N is a group and E E is a group of operators on N N then write d E ( N ) {d_E}(N) for the minimum number of elements needed to generate N N as an E E -group. It is shown that if N N is a normal subgroup of E E and E E acts on N N by conjugation, then d E ( N ) = d E ( N / N ′ ) {d_E}(N) = {d_E}(N/N’) if d E ( N ) {d_E}(N) is finite and there does not exist an infinite descending series of E E -normal subgroups N ′ = C 0 > C 1 > ⋯ N’ = {C_0} > {C_1} > \cdots with each C i / C i + 1 {C_i}/{C_{i + 1}} perfect. Both these conditions are, in general, necessary.
group of operators, Generators, relations, and presentations of groups, normal subgroups, Extensions, wreath products, and other compositions of groups, Derived series, central series, and generalizations for groups, generating conjugacy classes
group of operators, Generators, relations, and presentations of groups, normal subgroups, Extensions, wreath products, and other compositions of groups, Derived series, central series, and generalizations for groups, generating conjugacy classes
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