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 |
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Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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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. |
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ISSN: | 1895-1074 2391-5455 1644-3616 2391-5455 |
DOI: | 10.2478/s11533-013-0287-8 |