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Generalised quaternion groups and distributively generated near-rings

Published online by Cambridge University Press:  20 January 2009

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In this paper two major questions concerning generalised quaternion groups and distributively generated (d.g.) near-rings are investigated. The d.g. near-rings generated, respectively, by the inner automorphisms, automorphisms, and endomorphisms of the group are described. It is also shown that these morphism near-rings are local near-rings and contain no non-trivial idempotents. Finally, it is demonstrated that exactly 16 d.g. near-rings can be defined on a given generalised quaternion group.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1973