W. Guo, Yu. V. Lutsenko, A. N. Skiba, “On nonnilpotent groups in which every two 3-maximal subgroups are permutable”, Sibirsk. Mat. Zh., 2009, Volume 50, Number 6,Pages <nobr>1255

This article is cited in 12 papers

On nonnilpotent groups in which every two 3-maximal subgroups are permutable

W. Guo^a, Yu. V. Lutsenko^b, A. N. Skiba^b

^a Department of Mathematics, Xuzhou Normal University, Xuzhou, P. R. China
^b Francisk Skaryna Gomel State University, Faculty of Mathematics, Gomel', Bearus

Abstract: We describe the structure of finite nonnilpotent groups in which every two 3-maximal subgroups are permutable. In particular, we describe finite nonnilpotent groups in which all 2-maximal or all 3-maximal subgroups are normal.

Keywords: Sylow subgroup, Schmidt group, $n$-maximal subgroup, nilpotent group, supersoluble group, soluble group, permutable subgroup.

UDC: 512.542

Received: 10.09.2008