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- W1989686075 abstract "Let ν( G ) denote the number of conjugacy classes of non-normal subgroups of a group G . We prove that if G is a finite group and ν( G ) ≠ 0, then there is a cyclic subgroup C of prime power order contained in the centre of G such that the order of G / C is a product of at most ν( G ) + 1 primes. We also obtain a bound in the opposite direction, thus obtaining a criterion for a group to have a bounded number of conjugacy classes of non-normal subgroups. These results extend to infinite groups, with the subgroup C being the infinite Prüfer p -group, but only when G has finitely many non-normal subgroups. This is to be expected because of the existence of monsters of the type constructed by S. V. Ivanov and A. Yu. Ol'shanskii. The structure of groups with infinitely many non-normal subgroups falling into finitely many conjugacy classes is also studied." @default.
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- W1989686075 date "1999-04-01" @default.
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- W1989686075 title "Groups with a Bounded Number of Conjugacy Classes of Non-normal Subgroups" @default.
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- W1989686075 doi "https://doi.org/10.1006/jabr.1998.7690" @default.
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