IJPAM: Volume 83, No. 2 (2013)

ON THE FINITENESS PROPERTIES OF GROUPS

Z.S. Tabatabaei$^1$, M. Naghshinehfard$^2$
$^1$Department of Mathematics
Marvdasht Branch
Islamic Azad University
Marvdasht, 73711-13119, IRAN
$^2$Department of Mathematics
Jahrom Branch
Islamic Azad University
Jahrom, 74135-355, IRAN


Abstract. For an automorphism $\varphi$ of the group $G$, the connection between the centralizer $C_G(\varphi)$ and the commutator $[G, \varphi]$ is investigated and as a consequence of the Schur theorem it is shown that if $G/C_G(\varphi)$ and $G'$ are both finite, then so is $[G, \varphi]$.

Received: August 28, 2012

AMS Subject Classification: 20D45, 20F14, 20B05

Key Words and Phrases: autocommutator subgroup, Schur theorem, derived subgroup

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DOI: 10.12732/ijpam.v83i2.4 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 83
Issue: 2