On supersolvability of fatorized finite groups
Copyright policy )On supersolvability of fatorized finite groups
Summary: We investigate the structure of finite groups that are products of two supersolvable groups and gain a sufficient condition for a group to be supersolvable. Our main theorem is the following: Let the group \(G=HK\) be the product of the subgroups \(H\) and \(K\). Assume that \(H\) permutes with every maximal subgroup of \(K\) and \(K\) permutes with every maximal subgroup of \(H\). If \(H\) is supersolvable, and \(K\) is nilpotent and \(K\) is \(\delta\)-permutable in \(H\), where \(\delta\) is a complete set of Sylow subgroups of \(H\), then \(G\) is supersolvable. Some known results are generalized.
- Tianjin Polytechnic University China (People's Republic of)
products of supersolvable groups, permutable subgroups, Products of subgroups of abstract finite groups, factorized groups, Sylow subgroups, Maximal subgroups, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, maximal subgroups, supersolvability, finite groups
products of supersolvable groups, permutable subgroups, Products of subgroups of abstract finite groups, factorized groups, Sylow subgroups, Maximal subgroups, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, maximal subgroups, supersolvability, finite groups
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