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A reduction theorem for perfect locally finite minimal non-FC groups

Published online by Cambridge University Press:  01 March 1999

FELIX LEINEN
FELIX LEINEN
Affiliation:
Fachbereich Mathematik, Universität Mainz, D-55099 Mainz, Germany; e-mail: leinen@mat.mathematik.uni-mainz.de
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Abstract

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A group G is said to be a minimal non-FC group, if G contains an infinite conjugacy class, while every proper subgroup of G merely has finite conjugacy classes. The structure of imperfect minimal non-FC groups is quite well-understood. These groups are in particular locally finite. At the other end of the spectrum, a perfect locally finite minimal non-FC group must be a p-group. And it has been an open question for quite a while now, whether such groups exist or not.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 41 , Issue 1 , March 1999 , pp. 81 - 83
Copyright
1999 Glasgow Mathematical Journal Trust