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- W4247202363 abstract "A subgroup- and quotientgroup closed class D of groups is a Dietzmann class if the normal closure 〈xG〉 of an element x of an arbitrary group G is a D-group, provided that 〈x〉∈D and G induces on 〈xG〉 a D-group of automorphisms. For a set π of prime numbers, let Fπ denote the class of finite, LFπ that of locally finite π-groups. For any subgroup- and quotientgroup closed class X with Fπ⊆X⊆LFπ, let HX denote the class of hyper-X-groups, (HX)C that of groups with HX-conjugacy classes. We show that HX and (HX)C—in particular HFπ, (HFπ)C and (LFπ)C—are Dietzmann classes." @default.
- W4247202363 created "2022-05-12" @default.
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- W4247202363 date "2004-07-01" @default.
- W4247202363 modified "2023-09-27" @default.
- W4247202363 title "The Dietzmann property of some classes of groups with locally finite conjugacy classes" @default.
- W4247202363 doi "https://doi.org/10.1016/s0021-8693(04)00069-9" @default.
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