Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Almost regular involutory automorphisms of uniquely $ 2$-divisible groups

Author: Yoav Segev
Journal: Proc. Amer. Math. Soc. 139 (2011), 3445-3450
MSC (2010): Primary 20E36
Published electronically: March 4, 2011
MathSciNet review: 2813376
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that a uniquely $ 2$-divisible group that admits an almost regular involutory automorphism is solvable.

References [Enhancements On Off] (What's this?)

  • [A] M. Aschbacher, Finite group theory, Cambridge Studies in Advanced Mathematics, 10. Cambridge University Press, Cambridge, 1986. MR 895134 (89b:20001)
  • [DS] T. De Medts, Y. Segev, Identities in Moufang sets, Trans. Amer. Math. Soc. 360 (2008), no. 11, 5831-5852. MR 2425693 (2009f:20042)
  • [DST] T. De Medts, Y. Segev, K. Tent, Special Moufang sets, their root groups and their $ \mu$-maps, Proc. Lond. Math. Soc. (3) 96 (2008), no. 3, 767-791. MR 2407819 (2009d:20068)
  • [HM] B. Hartley, Th. Meixner, Periodic groups in which the centralizer of an involution has bounded order, J. Algebra 64 (1980), no. 1, 285-291. MR 575796 (81i:20049)
  • [K] L. G. Kovács, Groups with regular automorphisms of order $ 4$, Math. Zeitschr. 75 (1961), 277-294. MR 0123613 (23:A938)
  • [N] B. H. Neumann, Groups covered by permutable subsets, J. London Math. Soc. 29 (1954), 236-248. MR 0062122 (15:931b)
  • [S] Y. Segev, Toward the abelian root groups conjecture for special Moufang sets, Advances in Mathematics 223 (2010), 1545-1554. MR 2592502
  • [SW] Y. Segev, R. Weiss, On the action of the Hua subgroups in special Moufang sets, Math. Proc. Cambridge Philos. Soc. 144 (2008), no. 1, 77-84. MR 2388234 (2009a:20002)
  • [Sh] V. P. Shunkov, Periodic groups with an almost regular involution, Algebra and Logic 11 (1974), 260-272.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 20E36

Retrieve articles in all journals with MSC (2010): 20E36

Additional Information

Yoav Segev
Affiliation: Department of Mathematics, Ben-Gurion University, Beer-Sheva 84105, Israel

Keywords: Almost regular involutory automorphism, uniquely $2$-divisible group.
Received by editor(s): September 1, 2010
Published electronically: March 4, 2011
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society