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Inner mappings of Bruck loops

Published online by Cambridge University Press:  01 January 1998

ALEXANDER KREUZER
ALEXANDER KREUZER
Affiliation:
Mathematisches Institut, Technische Universität München, Arcisstr. 21, 80290 München, Germany
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Abstract

K-loops have their origin in the theory of sharply 2-transitive groups. In this paper a proof is given that K-loops and Bruck loops are the same. For the proof it is necessary to show that in a (left) Bruck loop the left inner mappings L(b)L(a) L(ab)−1 are automorphisms. This paper generalizes results of Glauberman [3], Kist [8] and Kreuzer [9].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 123 , Issue 1 , January 1998 , pp. 53 - 57
Copyright
Cambridge Philosophical Society 1998

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