Groups where each element is conjugate to its certain power

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 n th 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,...

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Veröffentlicht in:Central European journal of mathematics 2013, Vol.11 (10), p.1742-1749
1. Verfasser: Hegedűs, Pál
Format: Artikel
Sprache:eng
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Zusammenfassung: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 n th 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.
ISSN:1895-1074
2391-5455
1644-3616
2391-5455
DOI:10.2478/s11533-013-0287-8