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On metabelian groups

Published online by Cambridge University Press:  09 April 2009

N. D. Gupta  and
M. F. Newman
N. D. Gupta
Affiliation:
Department of Pure Mathematics School of General Studies
M. F. Newman
Affiliation:
The Australian National University Canberra, A.C.T.
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In this note we present some results on relationships between certain verbal subgroups of metabelian groups. To state these results explicitly we need some notation. As usual further [x, 0y] = x and [x, ky] = [x, (k—1)y, y] for all positive integers k. The s-th term γs(G) of the lower central series of a group G is the subgroup of G generated by [a1, … as] for all a1, … as, in G. A group G is metabelian if [[a11, a2], [a3, a4]] = e (the identity element) for all a1, a2, a3, a4, in G, and has exponent k if ak = e for all a in G.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 6 , Issue 3 , August 1966 , pp. 362 - 368
Copyright
Copyright © Australian Mathematical Society 1966

References

[1]Gruenberg, K. W., ‘The upper central series in soluble groups’, Illinois J. Math., 5 (1961) 436–466.CrossRefGoogle Scholar
[2]Kovács, L. G. and Newman, M. F., ‘On non-Cross varieties of groups’, in preparation.Google Scholar
[3]Weston, K. W., ‘The lower central series of metabelian Engel groups’, Notices Amer. Math. Soc., 12 (1965) 81.Google Scholar