Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-14T18:27:56.785Z Has data issue: false hasContentIssue false
  • English
  • Français

Conjugate purity and infinite groups

Published online by Cambridge University Press:  09 April 2009

Bola O. Balogun
Bola O. Balogun
Affiliation:
University of IfeIle-Ife Nigeria
Rights & Permissions [Opens in a new window]

Abstract

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 Balogun (1974), we proved that a finite group in which every subgroup is conjugately pure is necessarily Abelian and we left open the infinite case. In this paper we settle this problem positively for soluble, locally soluble groups and certain classes of groups which include the FC-groups. In the last section of this paper we characterize groups which are conjugately pure in every containing group.

Subject classification (Amer. Math. Soc. (MOS) 1970): 20 E 99.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1979 , pp. 9 - 14
Copyright
Copyright © Australian Mathematical Society 1979

References

Balogun, B. O. (1974), ‘Conjugately pure subgroup problems’, Amer. Math. Monthly 81, 156–158. (MR 48 ≠ 11332.)Google Scholar
Baumslag, G. (1969), ‘A non-cyclic one-relator group all of whose finite quotients are cyclic, J. Austral. Math. Soc. 10, 497–498.Google Scholar
Friesen, D. K. (1974), ‘Normal complements in finite solvable groups’, J. Austral. Math. Soc. 18, 262–264. (MR 51 ≠ 51749.)Google Scholar
Higman, G., Neumann, B. H. and Neumann, Hanna (1949), ‘Embedding theorems for groups’, J. London Math. Soc. 24, 247–254.Google Scholar
Huppert, B. (1967), Endliche Gruppen I (Die Grundlehren der Mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin, New York).CrossRefGoogle Scholar
Passman, D. S. (1968), Permutation groups (W. A. Benjamin Inc., New York, Amsterdam).Google Scholar
Robinson, D. J. S. (1972), Finiteness conditions and generalized soluble groups, Parts 1 and 2 (Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, Berlin, Heidelberg, New York).Google Scholar