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- W4385200414 abstract "Abstract A well-known theorem of Philip Hall states that if a group G has a nilpotent normal subgroup N such that $G/N'$ is nilpotent, then G itself is nilpotent. We say that a group class 𝔛 is a Hall class if it contains every group G admitting a nilpotent normal subgroup N such that $G/N'$ belongs to 𝔛. Hall classes have been considered by several authors, such as Plotkin [‘Some properties of automorphisms of nilpotent groups’, Soviet Math. Dokl. 2 (1961), 471–474] and Robinson [‘A property of the lower central series of a group’, Math. Z. 107 (1968), 225–231]. A further detailed study of Hall classes is performed by us in another paper [‘Hall classes of groups’, to appear] and we also investigate the behaviour of the class of finite-by-𝔜 groups for a given Hall class 𝔜 [‘Hall classes in linear groups’, to appear]. The aim of this paper is to prove that for most natural choices of the Hall class 𝔜, also the classes $(mathbf{L}mathfrak{F})mathfrak{Y}$ and 𝔅𝔜 are Hall classes, where L 𝔉 is the class of locally finite groups and 𝔅 is the class of locally finite groups of finite exponent." @default.
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- W4385200414 date "2023-07-24" @default.
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- W4385200414 title "HALL CLASSES OF GROUPS WITH A LOCALLY FINITE OBSTRUCTION" @default.
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- W4385200414 doi "https://doi.org/10.1017/s1446788723000071" @default.
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