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INVOLUTIONS IN LOCALLY FINITE GROUPS

Published online by Cambridge University Press:  29 March 2004

MAHMUT KUZUCUOĞLU  and
PAVEL SHUMYATSKY
MAHMUT KUZUCUOĞLU
Affiliation:
Department of Mathematics, Middle East Technical University, Ankara, 06531 [email protected]
PAVEL SHUMYATSKY
Affiliation:
Department of Mathematics, University of Brasilia, Brasilia-DF, 70910-900 [email protected]
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Abstract

The paper deals with locally finite groups $G$ having an involution $\phi$ such that $C_G(\phi)$ is of finite rank. The following theorem gives a very detailed description of such groups.

Let $G$ be a locally finite group having an involution $\phi$ such that $C_G(\phi)$ is of finite rank. Then $G/[G,\phi]$ has finite rank. Furthermore, $[G,\phi]'$ contains a characteristic subgroup $B$ such that the following hold.

(1) $B$ is a product of finitely many subgroups normal in $[G,\phi]$ isomorphic to either PSL$(2,K)$ or SL$(2,K)$ for some infinite locally finite fields $K$ of odd characteristic.

(2) $[G,\phi]'/B$ has finite rank.

Keywords

20E25
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 306 - 316
Copyright
The London Mathematical Society 2004

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