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- W4251070131 abstract "It is a known fact that the subgroup Ω2(G) generated by all elements of order at most 4 in a finite 2-group G has a strong influence on the structure of the whole group G. For example, if Ω2(G) is metacyclic, then G is also metacyclic (N. Blackburn). Here we consider the case Ω2(G) = C2 x D, where C2 is cyclic of order 2 and D is any 2-group of maximal class and we show that ❘G : Ω2(G)❘ ≤ 2 and the structure of G is uniquely determined. We determine also the structure of a finite 2-group G whose elements of order 4 generate the subgroup Ω*2 (G) ≅ C2 × Q2n, where Q2n is generalized quaternion of order 2n. Finally, we show that a finite p-group G all of whose non-cyclic subgroups are generated by elements of order p is cyclic or of exponent p or a dihedral 2-group." @default.
- W4251070131 created "2022-05-12" @default.
- W4251070131 creator A5061048354 @default.
- W4251070131 date "2004-01-06" @default.
- W4251070131 modified "2023-10-01" @default.
- W4251070131 title "Elements of order at most 4 in finite 2-groups" @default.
- W4251070131 doi "https://doi.org/10.1515/jgth.2004.7.4.431" @default.
- W4251070131 hasPublicationYear "2004" @default.
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