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Finite classical groups and multiplication groups of loops

Published online by Cambridge University Press:  24 October 2008

Ari Vesanen
Ari Vesanen
Affiliation:
Department of Mathematics, University of Oulu, 90570 Oulu, Finland
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Extract

Let Q be a loop; then the left and right translations La(x) = ax and Ra(x) = xa are permutations of Q. The permutation group M(Q) = 〈La, Ra | a ε Q〉 is called the multiplication group of Q; it is well known that the structure of M(Q) reflects strongly the structure of Q (cf. [1] and [8], for example). It is thus an interesting question, which groups can be represented as multiplication groups of loops. In particular, it seems important to classify the finite simple groups that are multiplication groups of loops. In [3] it was proved that the alternating groups An are multiplication groups of loops, whenever n ≥ 6; in this paper we consider the finite classical groups and prove the following theorems

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 3 , May 1995 , pp. 425 - 429
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

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