Abstract
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.
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