Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-26T01:45:59.740Z Has data issue: false hasContentIssue false
  • English
  • Français

Elliptically embedded subgroups and nilpotent products

Published online by Cambridge University Press:  18 May 2009

Howard Smith
Howard Smith
Affiliation:
Department Of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837, U.S.A.
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.

A recent paper of Rhemtulla and Wilson [4] is concerned with elliptically embedded subgroups of groups. A subgroup H of a group G is elliptically embedded in G if, for each subgroup K of G, there is some integer m such that (H, K) = (HK)m. Some sufficient conditions for elliptic embedding are given in Section 2 of [4], and some consequences of the presence of this property are to be found in Theorems 1 and 2 of the same paper and in the main theorem of [5]. It is evident from all of these results that the property of being elliptically embedded is closely related to the nilpotency and subnormality of certain subgroups. One of the questions considered here i s the following.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 3 , September 1989 , pp. 371 - 381
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

References

1.Blake, I. F. and Mullin, R. C.. The mathematical theory of coding (Academic Press, 1975).Google Scholar
2.Fuchs, L., Abelian groups (Pergamon Press, 1960).Google Scholar
3.Fuchs, L., Infinite abelian groups, Vol. 1 (Academic Press, 1970).Google Scholar
4.Rhemtulla, A. H. and Wilson, J. S., On elliptically embedded subgroups of soluble groups, Canad J. Math., 39 (1987), 956–68.CrossRefGoogle Scholar
5.Rhemtulla, A. H. and Wilson, J. S., Elliptically embedded subgroups of polycyclic groups, Proc. Amer. Math. Soc. 102 (1988), 230–34.CrossRefGoogle Scholar
6.Robinson, D. J. S., “A property of the lower central series of a group.” Math. Z., 107 (1968), 225–231.Google Scholar
7.Robinson, D. J. S., Finiteness conditions and generalized soluble groups. (Springer Verlag, 1972).CrossRefGoogle Scholar
8.Smith, H., Commutator subgroups of a join of subnormal subgroups, Arch. Math. (Basel), 41 (1983), 193–198.CrossRefGoogle Scholar
9.Smith, H., Group-theoretic properties inherited by lower central factors, Glasgow J. Math., 29 (1987), 89–91.CrossRefGoogle Scholar
10.Williams, J. P., The join of several subnormal subgroups, Math. Proc. Camb. Phil. Soc, 92 (1982), 391–399.CrossRefGoogle Scholar
11.Williams, J. P., Conditions for subnormality of a join of subnormal subgroups, Math. Proc. Camb. Phil. Soc., 92 (1982), 401–417.CrossRefGoogle Scholar