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On the structure and number of small Frattini Bol 2-loops

Published online by Cambridge University Press:  01 December 2006

GÁBOR P. NAGY
GÁBOR P. NAGY
Affiliation:
Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary.
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Abstract

Analogously to extraspecial $p$-groups, we define the class of small Frattini $p$-loops and investigate some properties of small Frattini Bol 2-loops. We show that they are related to certain invariant transversals in extraspecial 2-groups. This fact enables us to describe the automorphisms and isomorphisms of small Frattini Bol 2-loops by linear algebraic tools. We use this description to obtain a lower bound for the number of non-isomorphic small Frattini Bol 2-loops of given order.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 141 , Issue 3 , November 2006 , pp. 409 - 419
Copyright
© 2006 Cambridge Philosophical Society

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