Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2010; 47(4): 687-691

Printed July 1, 2010

https://doi.org/10.4134/BKMS.2010.47.4.687

Copyright © The Korean Mathematical Society.

On groups satisfying the maximal and the minimal conditions for subnormal subgroups of infinite order or index

Alessio Russo

Seconda Universit\`a di Napoli

Abstract

In this article we will prove that a generalized radical group satisfying the maximal condition for subnormal subgroups of infinite order (the minimal condition for subnormal subgroups of infinite index, respectively) is soluble-by-finite. Such result generalizes that obtained by D. H. Paek in [5].

Keywords: subnormal, maximal condition, minimal condition, soluble, subsoluble, radical

MSC numbers: Primary 20E15; Secondary 20F22