On the normal index of maximal subgroups in finite groups (Q912978)
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scientific article; zbMATH DE number 4146239
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the normal index of maximal subgroups in finite groups |
scientific article; zbMATH DE number 4146239 |
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On the normal index of maximal subgroups in finite groups (English)
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1990
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The author uses results from primitive group theory to generalize some work of Beidleman and Spencer, Mukherjee, and Mukherjee and Bhattacharya on criteria for solvability, supersolvability, and nilpotency to \(\Pi\)- solvability, \(\Pi\)-supersolvability, and \(\Pi\)-nilpotency. Typical is Theorem 1: Let \(\Pi\) be a set of primes. If finite group G has a \(\Pi\)- solvable maximal subgroup M whose normal index equals its index in G, then G is \(\Pi\)-solvable.
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\(\Pi \) -solvability
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\(\Pi \) -supersolvability
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\(\Pi \) -nilpotency
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\(\Pi \) -solvable maximal subgroup
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normal index
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