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- W2335331984 abstract "Let p be a prime and P be a p -subgroup of a finite group G . Suppose that g ∈ G and that P ∩ P g has index p in P . In [ 4 ], we assumed that g normalizes no non-identity normal subgroup of P . We obtained some bounds on the order of P and some applications to the case in which p = 2 and P is a Sylow 2-subgroup of 〈 P, P g 〉. In this paper, we examine this situation further by considering the isomorphism ϕ of P ∩ P g -l onto P ∩ P g given by ϕ ( x ) = x g . We actually consider arbitrary isomorphisms ϕ between two subgroups of index p in P . However, an easy argument (Lemma 2.3) shows that every such ϕ can be obtained as above for some G and some g . We obtain some results concerning the nilpotence class rather than the order of P ." @default.
- W2335331984 created "2016-06-24" @default.
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- W2335331984 date "1971-12-01" @default.
- W2335331984 modified "2023-10-18" @default.
- W2335331984 title "Isomorphic Subgroups of Finite <i>p</i>-Groups. I" @default.
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- W2335331984 doi "https://doi.org/10.4153/cjm-1971-106-0" @default.
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