$p$-solvable groups with few automorphism classes of subgroups of order $p$
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- by Fletcher Gross PDF
- Proc. Amer. Math. Soc. 30 (1971), 437-444 Request permission
Abstract:
This paper investigates the relationship between the p-length, ${l_p}(G)$, of the finite p-solvable group G and the number, ${a_p}(G)$, of orbits in which the subgroups of order p are permuted by the automorphism group of G. If $p > 2$ and ${a_p}(G) \leqq 2$, it is shown that ${l_p}(G) \leqq {a_p}(G)$. If $p = 2$ and ${a_2}(G) = 1$, it is proved that either ${l_p}(G) \leqq {a_p}(G)$ or $G/{O_{2β}}(G)$ is a specific group of order 48.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 437-444
- MSC: Primary 20.40
- DOI: https://doi.org/10.1090/S0002-9939-1971-0286887-6
- MathSciNet review: 0286887