Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-25T09:03:34.687Z Has data issue: false hasContentIssue false

Note on operations generating the group operations in nilpotent groups of class 3

Published online by Cambridge University Press:  09 April 2009

Ernest Plonka
Affiliation:
Instytut Matematyczny PAN 51–617 Wroclaw ul. Kopernika 18 Poland
Rights & Permissions [Opens in a new window]

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.

Let K be a class of groups and let ω(K) denote the set of all such words w(x, y) that the group operations 1, x-1, xy in every group GK can be expressed as a superposition of w and the projections e1(x, y) = x, e2(x, y) = y.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1975

References

Fajtlowicz, S. (1972), ‘On fundamental operations in groups’, J. Austral. Math. Soc. 14, 445457.CrossRefGoogle Scholar
Hulanicki, A. and Swierzkowski, S. (1962), ‘On group operations other than xy or yx’, Publ. Math. Debrecen 9, 4248.Google Scholar
Huppert, B. (1967), Endliche Gruppen I, (Springer Verlag, 1967).CrossRefGoogle Scholar
Padmanabhan, P. (1969), ‘A note on inverse binary operation in abelian groupsFund. Math. 65, 6163.CrossRefGoogle Scholar