The number of solutions of xp = 1 in a finite group
Published online by Cambridge University Press: 24 October 2008
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.
- 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
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