Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-27T23:20:11.965Z Has data issue: false hasContentIssue false
  • English
  • Français

A problem on growth sequences of groups

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

A. Erfanian
A. Erfanian
Affiliation:
No. 31, 25th EdalatAhamd Abab Ave, Mashhad, Iran
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.

The aim of this paper is to consider Problem 1 posed by Stewart and Wiegold in [6]. The main result is that if G is a finitely generated perfect group having non-trivial finite images, then there exists a finite image B of G such that the growth sequence of B is eventuallly faster than that of every finite image of G. Moreover we investigate the growth sequences of simple groups of the same order.

MSC classification

Secondary: 20F05: Generators, relations, and presentations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 2 , October 1995 , pp. 283 - 286
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Artin, E., ‘The orders of the classical simple groups’, Comm. Pure Appl. Math. 8 (1955), 455–472.Google Scholar
[2]Aschbacher, M., ‘On the maximal subgroups of the finite classical groups’, Invent. Math. 76 (1984), 469–514.CrossRefGoogle Scholar
[3]Gaschütz, W., ‘Zu einem von B. H. and H. Neumann gestellten problem,’ Math. Nachr. 14 (1955), 249–252.Google Scholar
[4]Liebeck, M. W., Praeger, C. E. and Saxl, J., ‘The maximal factorizations of the finite simple groups and their automorphism groups’, Mem. Amer. Math. Soc. No.432 (1990), 17–23.Google Scholar
[5]Meier, D. and James, Wiegold, ‘Growth sequences of finite groups V’, J. Austral. Math. Soc. (Series A) 31 (1981), 374–375.Google Scholar
[6]Stewart, A. G. R. and James, Wiegold, ‘Growth sequences of fintely generated groups II’, Bull. Austral. Math. Soc. 40 (1989), 323–329.Google Scholar
[7]Wiegold, J., ‘Growth sequences of finite groups’, J. Austral. Math. Soc. 17 (1974), 133–141.CrossRefGoogle Scholar
[8]Wiegold, J., ‘Growth sequences of finite groups II’, J. Austral. Math. Soc. (Series A) 20 (1975), 225–229.CrossRefGoogle Scholar
[9]Wiegold, J., ‘Growth sequences of finite groups III’, J. Austral. Math. Soc. (Series A) 25 (1978), 142–144.CrossRefGoogle Scholar
[10]Wiegold, J., ‘Growth sequences of finite groups IV’, J. Austral. Math. Soc. (Series A) 29 (1980), 14–16.CrossRefGoogle Scholar
[11]James, Wiegold and Wilson, J. S., ‘Growth sequences of finitely generated groups’, Arch. Math. 30 (1978), 337–343.Google Scholar