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EMBEDDING GROUPS OF CLASS TWO AND PRIME EXPONENT IN CAPABLE AND NONCAPABLE GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  13 March 2009

ARTURO MAGIDIN
ARTURO MAGIDIN*
Affiliation:
Mathematics Dept., University of Louisiana–Lafayette, 217 Maxim Doucet Hall, PO Box 41010, Lafayette LA 70504-1010, USA (email: magidin@member.ams.org)
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Abstract

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We show that if G is any p-group of class at most two and exponent p, then there exist groups G1 and G2 of class two and exponent p that contain G, neither of which can be expressed as a central product, and with G1 capable and G2 not capable. We provide upper bounds for rank(Giab) in terms of rank(Gab) in each case.

Keywords

capablep-group2-nilpotent

MSC classification

Secondary: 20D15: Nilpotent groups, $p$-groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 2 , April 2009 , pp. 303 - 308
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

The author was supported by a grant from the Louisiana Board of Regents Support Fund.

References

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