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Factorized Groups with max, min and min-p

Published online by Cambridge University Press:  20 November 2018

Bernhard Amberg
Bernhard Amberg*
Affiliation:
Fachbereich Mathematik, Universität MainzD-6500 Mainz, West Germany
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Abstract

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Let be a class of groups which is closed under the forming of subgroups, epimorphic images and extensions. It is shown that every soluble product G = AB of two -subgroups A and B, one of which satisfies max or min, is an -group (Theorem A). If X satisfies an additional requirement, then every soluble product G = AB of two -subgroups A and B, one of which is a torsion group with min-p for every prime p, is an -group (Theorem B). Corollary: Every soluble product G = AB of two π-subgroups A and B with min-p for every prime p in the set of primes π, is a π -group with min-p for every p.

Keywords

20 E 22 (also 20 F 16)
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 2 , 01 June 1984 , pp. 171 - 178
Copyright
Copyright © Canadian Mathematical Society 1984

References

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