Abstract
This paper deals with a rationality condition for groups. Let n be a fixed positive integer. Suppose every element g of the finite solvable group is conjugate to its nth power g n. Let p be a prime divisor of the order of the group. We conclude that the multiplicative order of n modulo p is small, or p is small.
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Hegedűs, P. Groups where each element is conjugate to its certain power. centr.eur.j.math. 11, 1742–1749 (2013). https://doi.org/10.2478/s11533-013-0287-8
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DOI: https://doi.org/10.2478/s11533-013-0287-8