Automorphism of a finite group scalar on the cosets of a subgroup
HTML articles powered by AMS MathViewer
- by Saïd Sidki PDF
- Proc. Amer. Math. Soc. 32 (1972), 399-402 Request permission
Abstract:
Let G be a finite group, $\sigma$ an automorphism of G, M a $\sigma$-invariant subgroup of G, and n a fixed integer. If $\sigma (g) \in {g^n}M$ for all $g \in G$ then there exists a $\sigma$-invariant normal subgroup K of G, contained in M, with $\sigma (g) \in {g^n}K$ for all $g \in G$.References
- J. L. Alperin, A classification of $n$-abelian groups, Canadian J. Math. 21 (1969), 1238–1244. MR 248204, DOI 10.4153/CJM-1969-136-1
- Christopher D. H. Cooper, Power automorphisms of a group, Math. Z. 107 (1968), 335–356. MR 236253, DOI 10.1007/BF01110066
- Walter Feit and John G. Thompson, Solvability of groups of odd order, Pacific J. Math. 13 (1963), 775–1029. MR 166261
- Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
- Eugene Schenkman, Group theory, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1965. MR 0197537
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 399-402
- MSC: Primary 20D45
- DOI: https://doi.org/10.1090/S0002-9939-1972-0301096-0
- MathSciNet review: 0301096