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J. Sib. Fed. Univ. Math. Phys., 2013, Volume 6, Issue 4, Pages 437–440 (Mi jsfu329)  

Construction of some simple locally finite groups

Ülviye B. Güvena, Otto H. Kegelb, Mahmut Kuzucuoğlua

a Department of Mathematics, Middle East Technical University, Ankara, 06 531 Turkey
b Mathematisches Institut, Eckerstr. 1, Albert-Ludwigs-Universitat Freiburg, Eckerstrabe, 1, Freiburg, D-79104, Germany

Abstract: We construct a proper class of simple locally finite groups. Namely for each infinite cardinal $\kappa$, we construct uncountably many pairwise non-isomorphic simple locally finite groups of cardinality $\kappa$, as a direct limit of finitary symmetric groups. The construction of the groups of similar kind for countably infinite order has been common knowledge as indicated in [2]. The countable ones are classified using the lattice of Steinitz numbers by Kroshko–Sushchansky in [3]. We give the classification of the uncountable ones by the pair, the cardinality of the group and the characteristic which corresponds to a Steinitz number. We study the structure of the centralizers of arbitrary elements in this new class of groups and correct some of the errors in the section about the centralizers of elements in $S(\xi)$ in [3].

Keywords: simple locally finite group, Steinitz number, construction.

Full text: PDF file (133 kB)
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UDC: 517.2
Received: 04.08.2013
Received in revised form: 15.09.2013
Accepted: 16.10.2013
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Citation: Ülviye B. Güven, Otto H. Kegel, Mahmut Kuzucuoğlu, “Construction of some simple locally finite groups”, J. Sib. Fed. Univ. Math. Phys., 6:4 (2013), 437–440

Citation in format AMSBIB
\Bibitem{GuvKegKuz13}
\by \"Ulviye~B.~G\"uven, Otto~H.~Kegel, Mahmut Kuzucuo{\u g}lu
\paper Construction of some simple locally finite groups
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2013
\vol 6
\issue 4
\pages 437--440
\mathnet{http://mi.mathnet.ru/jsfu329}


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