Abstract.
The following theorem is proved. Let G be a finite group of odd order admitting an involutory automorphism φ. Suppose that G has derived length d and that C G (φ) is nilpotent of class c. Assume that C G (φ) is a m-generator. Then [G,φ]′ is nilpotent of {c,d,m}-bounded class.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
AO Asar (1981) ArticleTitleInvolutory automorphisms of groups of odd order. Arch Math 36 97–103 Occurrence Handle10.1007/BF01223675
W Feit JG Thompson (1963) ArticleTitleSolvability of groups of odd order. Pacific J Math 13 773–1029
P Hall (1958) ArticleTitleSome sufficient conditions for a group to be nilpotent. Illinois J Math 2 787–801
B Hartley Th. Meixner (1980) ArticleTitlePeriodic groups in which the centralizer of an involution has bounded order. J Algebra 64 285–291 Occurrence Handle10.1016/0021-8693(80)90147-7
Huppert B (1967) Endliche Gruppen. Berlin: Springer
LG Kovacs GE Wall (1966) ArticleTitleInvolutory automorphisms of groups of odd order and their fixed point groups. Nagoya Math J 27 113–120
P Shumyatsky (1996) ArticleTitleInvolutory automorphisms of periodic groups. Internat J Algebra Comput 6 745–749 Occurrence Handle10.1142/S0218196796000428
P Shumyatsky (1998) ArticleTitleInvolutory automorphisms of finite groups and their centralizers. Arch Math (Basel) 71 425–432
JN Ward (1966) ArticleTitleInvolutory automorphisms of groups of odd order. J Austral Math Soc 6 480–494
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shumyatsky, P. Involutory Automorphisms of Groups of Odd Order. Mh Math 146, 77–82 (2005). https://doi.org/10.1007/s00605-004-0289-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00605-004-0289-5