A constructive approach: From local subgroups to new classes of finite groups
Copyright policy )A constructive approach: From local subgroups to new classes of finite groups
Let G be a finite group and S be a proper subgroup of G. A group G is called an S-(S-quasinormal)-group if every local subgroup of G is either an S-quasinormal subgroup or conjugate to a subgroup of S. The main purpose of this construction is to demonstrate a new way of analyzing the structure of a finite group by the properties and the number of conjugacy classes of its local subgroups.
- China Agricultural University China (People's Republic of)
Matematik, local subgroups;simple groups;solvable groups;S-quasinormal subgroups, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, \(\mathrm{S}\)-quasinormal subgroups, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, Finite simple groups and their classification, simple groups, Mathematical Sciences, local subgroups, solvable groups
Matematik, local subgroups;simple groups;solvable groups;S-quasinormal subgroups, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, \(\mathrm{S}\)-quasinormal subgroups, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, Finite simple groups and their classification, simple groups, Mathematical Sciences, local subgroups, solvable groups
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