Hostname: page-component-7f64f4797f-m2b9p Total loading time: 0 Render date: 2025-11-04T11:29:20.519Z Has data issue: false hasContentIssue false
  • English
  • Français

The number of solutions of xp = 1 in a finite group

Published online by Cambridge University Press:  24 October 2008

Thomas J. Laffey
Thomas J. Laffey
Affiliation:
University College, Dublin
Get access Rights & Permissions [Opens in a new window]

Extract

Let G be a finite group, p a prime divisor of |G| and suppose that G is not a p-group. In this note, we show that the number of elements x ∈ G such that xp = 1 is at most (p|G|)/(p + 1). This answers a question posed by D. MacHale. When G is a Frobenius group of order p(p + 1), p a Mersenne prime, the above bound is attained.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 2 , September 1976 , pp. 229 - 231
Copyright
Copyright © Cambridge Philosophical Society 1976

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

(1)Gorenstein, D.Finite groups (New York, Harper and Row, 1968).Google Scholar
(2)Liebeck, H. and MacHale, D.Groups with automorphisms inverting most elements. Math. Z. 124 (1972), 51–63.CrossRefGoogle Scholar