Groups where each element is conjugate to its certain power

• Autorzy: Pál Hegedűs
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Finite solvable groups; Conjugacy criterion; Rationality

Kategorie tematyczne

• 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, π -length, ranks
• 20E45: Conjugacy classes
• 20C20: Modular representations and characters

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 10
• Strony: 1742-1749

Daty

wydano

2013-10-01

online

2013-07-20

Twórcy

autor

Pál Hegedűs

• Department of Mathematics and its Applications, Central European University, Nádor u. 9, Budapest, 1051, Hungary

Bibliografia

• [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] 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]
• [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] 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]

Identyfikatory

DOI

10.2478/s11533-013-0287-8