1.Previous
3.Next

group, the index [G:?_k(G)] is equal to the order of ?_k(G). In fact, commutators and powers interact in particularly simple ways . For example, given normal subgroups M and N of a regular p-group G and nonnegative integers m and n, one has [?_m(M),?_n(N)] = ?_m+n([M,N]).
* Philip Hall's criteria of regularity of a p-group G: G is regular, if one of the following hold:
*# [G:?₁(G)] <

1.Previous
3.Next