Abstract
An involution i of a group G is said to be almost perfect in G if any two involutions of iG the order of a product of which is infinite are conjugated via a suitable involution in iG. We generalize a known result by Brauer, Suzuki, and Wall concerning the structure of finite groups with elementary Abelian centralizers of involutions to groups with almost perfect involutions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Brauer, M. Suzuki, and G. E. Wall, “A characterization of the one-dimensional unimodular projective groups over finite fields,” Ill. J. Math., 2, No. 3, 718–742 (1958).
V. D. Mazurov, “Infinite groups with Abelian centralizers of involutions,” Algebra Logika, 39, No. 1, 74–86 (2000).
N. M. Suchkov, “Periodic groups with Abelian centralizers of involutions,” Mat. Sb., 193, No. 2, 153–160 (2002).
M. Suzuki, “On characterizations of linear groups. I,” Trans. Am. Math. Soc., 92, 191–219 (1959).
A. I. Sozutov, “Frobenius pairs with perfect involutions,” Algebra Logika, 44, No. 6, 751–762 (2005).
V. D. Mazurov, “2-Transitive permutation groups,” Sib. Mat. Zh., 31, No. 4, 102–104 (1990).
Author information
Authors and Affiliations
Additional information
__________
Translated from Algebra i Logika, Vol. 46, No. 1, pp. 75–82, January–February, 2007.
Rights and permissions
About this article
Cite this article
Sozutov, A.I., Kryukovskii, A.S. Groups with elementary Abelian centralizers of involutions. Algebr Logic 46, 46–49 (2007). https://doi.org/10.1007/s10469-007-0005-3
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10469-007-0005-3