Groups where each element is conjugate to its certain power

Pál Hegedűs

Open Mathematics (2013)

  • Volume: 11, Issue: 10, page 1742-1749
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Pál Hegedűs. "Groups where each element is conjugate to its certain power." Open Mathematics 11.10 (2013): 1742-1749. <http://eudml.org/doc/269283>.

@article{PálHegedűs2013,
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.},
author = {Pál Hegedűs},
journal = {Open Mathematics},
keywords = {Finite solvable groups; Conjugacy criterion; Rationality; finite solvable groups; conjugacy classes; rationality},
language = {eng},
number = {10},
pages = {1742-1749},
title = {Groups where each element is conjugate to its certain power},
url = {http://eudml.org/doc/269283},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Pál Hegedűs
TI - Groups where each element is conjugate to its certain power
JO - Open Mathematics
PY - 2013
VL - 11
IS - 10
SP - 1742
EP - 1749
AB - 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.
LA - eng
KW - Finite solvable groups; Conjugacy criterion; Rationality; finite solvable groups; conjugacy classes; rationality
UR - http://eudml.org/doc/269283
ER -

References

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  1. [1] Farias e Soares E., Big primes and character values for solvable groups, J. Algebra, 1986, 100(2), 305–324 http://dx.doi.org/10.1016/0021-8693(86)90079-7[Crossref] 
  2. [2] Gow R., Groups whose characters are rational-valued, J. Algebra, 1976, 40(1), 280–299 http://dx.doi.org/10.1016/0021-8693(76)90098-3[Crossref] Zbl0348.20017
  3. [3] Huppert B., Endliche Gruppen I, Grundlehren Math. Wiss., 134, Springer, Berlin-New York, 1967 http://dx.doi.org/10.1007/978-3-642-64981-3[Crossref] 
  4. [4] Huppert B., Blackburn N., Finite Groups III, Grundlehren Math. Wiss., 243, Springer, Berlin-New York, 1982 http://dx.doi.org/10.1007/978-3-642-67997-1[Crossref] 

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