Hall-closure and products of Fitting classes

Journal of the Australian Mathematical Society

Owen J. Brison¹ 

关键词: 20 D 10;    20 D 25;    20 E 22;   

DOI  :  10.1017/S1446788700024502

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

The Fitting class (of finite, soluble, groups), , is said to be Hall π-closed (where π is a set of primes) if whenever G is a group inand H is a Hall π-subgroup of G, then H belongs to . In this paper, we study the Hall π-closure of products of Fitting classes. Our main result is a characterisation of the Hall π-closedFitting classes of the form (wheredenotes the so-called smallest normal Fitting class), subject to a restriction connecting π with the characteristic of . We also characterise those Fitting classes(respectively, ) such that(respectively, ) is Hall π-closed for all Fitting classes . In each case, part of the proof uses a concrete group construction. As a bonus, one of these construction also yields a “cancellation result” for certain products of Fitting classes.

【 授权许可】

Unknown