Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-19T22:07:16.803Z Has data issue: false hasContentIssue false
  • English
  • Français

Periodic groups with permutable subgroup products

Published online by Cambridge University Press:  24 October 2008

Patrizia Longobardi ,
Mercede Maj  and
Akbar Rhemtulla
Patrizia Longobardi
Affiliation:
Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli, Via Mezzocannone 8, 80134 Naples, Italy
Mercede Maj
Affiliation:
Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli, Via Mezzocannone 8, 80134 Naples, Italy
Akbar Rhemtulla
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, CanadaT6G 2G1
Get access Rights & Permissions [Opens in a new window]

Abstract

Let G be a group. If there exists an integer n > 1 such that for each n-tuple (H1, …, Hn) of subgroups of G there is a non-identity permutation σ of Σn such that the complexes H1,…Hn and Hσ(1)…Hσ(n) are equal, then G is said to have the property of permutable subgroup products, or to be a PSP group. We show that periodic groups with this property are locally finite and investigate the structure of such groups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 3 , November 1989 , pp. 431 - 437
Copyright
Copyright © Cambridge Philosophical Society 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Blyth, R. D.. Rewriting products of group elements. I. J. Algebra 116 (1988), 506–521.Google Scholar
[2]Blyth, R. D.. Rewriting products of group elements. II. J. Algebra 118 (1988), 246–259.CrossRefGoogle Scholar
[3]Blyth, R. D. and Robinson, D. J. S.. Recent progress on rewritability in groups. In Proceedings of the 1987 Singapore Group Theory Conference (Walter de Gruyter, 1989), pp. 77–85.Google Scholar
[4]Cooper, D. H.. Power automorphisms of a group. Math. Z. 107 (1968), 335–356.CrossRefGoogle Scholar
[5]Curzio, M., Longobardi, P. and Maj, M.. Su di un problema combinatorio in teoria dei gruppi. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 74 (1983), 136–142.Google Scholar
[6]Curzio, M., Longobardi, P., Maj, M. and Robinson, D. J. S.. A permutational property of groups. Arch. Math. (Basel) 44 (1985), 385–389.CrossRefGoogle Scholar
[7]Iwasawa, K.. Über die endlichen Gruppen und die Verbände ihrer Untergruppen. J. Univ. Tokyo 3 (1941), 171–199.Google Scholar
[8]Iwasawa, K.. On the structure of infinite M-groups. Japan. J. Math. 18 (1943), 709–728.CrossRefGoogle Scholar
[9]Maj, M.. Some remarks on groups with permutable subgroup products. (To appear.)Google Scholar
[10]Rhbmtulla, A. H. and Weiss, A. R.. Groups with permutable subgroup products. In Proceedings of the 1987 Singapore Group Theory Conference (Walter de Gruyter, 1989), pp. 485–495.Google Scholar
[11]Robinson, D. J. S.. Finiteness conditions and generalized soluble groups, vol. 1 (Springer-Verlag, 1972).Google Scholar
[12] M.Tomkinson, J.. FC-Groups. Research Notes in Math. no. 96 (Pitman, 1984).Google Scholar