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- W2130059413 abstract "Abstract c -Sections of maximal subgroups in a finite group and their relation to solvability have been extensively researched in recent years. A fundamental result due to Wang [‘C-normality of groups and its properties’, J. Algebra 180 (1998), 954–965] is that a finite group is solvable if and only if the c -sections of all its maximal subgroups are trivial. In this paper we prove that if for each maximal subgroup of a finite group G , the corresponding c -section order is smaller than the index of the maximal subgroup, then each composition factor of G is either cyclic or isomorphic to the O’Nan sporadic group (the converse does not hold). Furthermore, by a certain ‘refining’ of the latter theorem we obtain an equivalent condition for solvability. Finally, we provide an existence result for large subgroups in the sense of Lev [‘On large subgroups of finite groups’ J. Algebra 152 (1992), 434–438]." @default.
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- W2130059413 date "2012-04-03" @default.
- W2130059413 modified "2023-09-25" @default.
- W2130059413 title "c-SECTIONS, SOLVABILITY AND LARGE SUBGROUPS OF FINITE GROUPS" @default.
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- W2130059413 doi "https://doi.org/10.1017/s0004972712000081" @default.
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