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ON LATTICES OF RADICALS IN THE CLASS OF ALL FINITE GROUPS

Part of: Representation theory of groups Radicals and radical properties of rings

Published online by Cambridge University Press:  16 February 2012

JAN KREMPA  and
IZABELA AGATA MALINOWSKA
JAN KREMPA*
Affiliation:
Institute of Mathematics, University of Warsaw ul. Banacha 2, 02-097 Warszawa, Poland (email: jkrempa@mimuw.edu.pl)
IZABELA AGATA MALINOWSKA
Affiliation:
Institute of Mathematics, University of Białystok, ul. Akademicka 2, 15-267 Białystok, Poland (email: izabelam@math.uwb.edu.pl)
*
✉For correspondence; e-mail: jkrempa@mimuw.edu.pl
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Abstract

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Lattices of radicals have been extensively studied, for example in the class of associative rings, leading to some interesting results. In this paper we investigate the lattice L of all radicals in the class of all finite groups. We also consider some of its important sublattices. In particular, we prove that the lattice L is closed to being modular, the lattice Lh of all hereditary radicals is a Boolean algebra, and there exists a natural, useful projection of the lattice L onto Lh.

Keywords

finite groupsradicalshereditary radicalssimple groupslattices of radicalsbalanced lattices

MSC classification

Secondary: 20D30: Series and lattices of subgroups 16N80: General radicals and rings
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 3 , December 2012 , pp. 495 - 505
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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