Generalised quaternion groups and distributively generated near-rings

J. J. Malone

doi:10.1017/S0013091500009974

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Malone, J. J. 1977. More on groups in which each element commutes with its endomorphic images. Proceedings of the American Mathematical Society, Vol. 65, Issue. 2, p. 209.

Meldrum, J. D. P. 1977. The endomorphism near-ring of an infinite dihedral group. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 76, Issue. 4, p. 311.

Meldrum, J. D. P. and Lyons, C. 1978. Characterizing series for faithful d.g. near-rings. Proceedings of the American Mathematical Society, Vol. 72, Issue. 2, p. 221.

Fong, Y. and Meldrum, J. D. P. 1980. The endomorphism near-rings of the symmetric groups of degree at least five. Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Vol. 30, Issue. 1, p. 37.

Malone, J. J. 1983. The group of automorphisms of a distributively generated near ring. Proceedings of the American Mathematical Society, Vol. 88, Issue. 1, p. 11.

Mason, Gordon 1985. Near-rings of mappings on finite topological groups. Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Vol. 38, Issue. 1, p. 92.

Lyons, Carter G. and Peterson, Gary L. 1988. Local endomorphism near-rings. Proceedings of the Edinburgh Mathematical Society, Vol. 31, Issue. 3, p. 409.

Cannon, G. Alan 1995. Near-Rings and Near-Fields. p. 89.

Saad, Gerhard Thomsen, Momme Johs and Syskin, Sergei A. 1995. Near-Rings and Near-Fields. p. 227.

Scott, S. D. 1995. Near-Rings and Near-Fields. p. 239.

Malone, J. J. 1995. Near-Rings and Near-Fields. p. 31.

Peterson, Gary L. and Scott, Stuart D. 2012. Units of compatible nearrings, II. Monatshefte für Mathematik, Vol. 167, Issue. 2, p. 273.

Pogorelov, Boris Aleksandrovich and Pudovkina, Marina Aleksandrovna 2021. Свойства регулярных представлений неабелевых $2$-групп с циклической подгруппой индекса $2$. Математические вопросы криптографии, Vol. 12, Issue. 4, p. 65.

Article contents

Generalised quaternion groups and distributively generated near-rings

Extract

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests