ON H-BASES AND H-DECOMPOSITIONS OF THE FINITE SOLVABLE AND ALTERNATING GROUPS

[摘要] Let G be a finite group such that every composition factor of G is either cyclic or isomorphic to the alternating group on n letters for some integer n. Then for every positive integer h there is a subset A subset-is-equal-to G such that \A\ less-than-or-equal-to (2h - 1)\G\1/h and A(h) = G. The following generalization for the group G also holds: For every positive integer h and any nonnegative real numbers alpha1, alpha2, ..., alpha(h) so that alpha1 + alpha2 + ... + alpha(h) = 1 there are subsets A1, A2, ..., A(h) subset-or-equal-to G such that \A1\ less-than-or-equal-to \G\alpha1, \A(i)] less-than-or-equal-to 2 \G\alpha(i) for 2 less-than-or-equal-to i less-than-or-equal-to h and A1A2 ... A(h) = G. In particular, the above conclusions hold if G is finite group and either G is an alternating group or G is solvable. (C) 1994 Academic Press, Inc.

[发布日期] 1994-12-01