A solvability criterion for finite groups related to character degrees
Babak Miraali; Sajjad Mahmood Robati
Czechoslovak Mathematical Journal (2020)
- Volume: 70, Issue: 4, page 1205-1209
- ISSN: 0011-4642
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topMiraali, Babak, and Robati, Sajjad Mahmood. "A solvability criterion for finite groups related to character degrees." Czechoslovak Mathematical Journal 70.4 (2020): 1205-1209. <http://eudml.org/doc/297305>.
@article{Miraali2020,
abstract = {Let $m>1$ be a fixed positive integer. In this paper, we consider finite groups each of whose nonlinear character degrees has exactly $m$ prime divisors. We show that such groups are solvable whenever $m>2$. Moreover, we prove that if $G$ is a non-solvable group with this property, then $m=2$ and $G$ is an extension of $\{\rm A\}_7$ or $\{\rm S\}_7$ by a solvable group.},
author = {Miraali, Babak, Robati, Sajjad Mahmood},
journal = {Czechoslovak Mathematical Journal},
keywords = {non-solvable group; solvable group; character degree},
language = {eng},
number = {4},
pages = {1205-1209},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A solvability criterion for finite groups related to character degrees},
url = {http://eudml.org/doc/297305},
volume = {70},
year = {2020},
}
TY - JOUR
AU - Miraali, Babak
AU - Robati, Sajjad Mahmood
TI - A solvability criterion for finite groups related to character degrees
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 4
SP - 1205
EP - 1209
AB - Let $m>1$ be a fixed positive integer. In this paper, we consider finite groups each of whose nonlinear character degrees has exactly $m$ prime divisors. We show that such groups are solvable whenever $m>2$. Moreover, we prove that if $G$ is a non-solvable group with this property, then $m=2$ and $G$ is an extension of ${\rm A}_7$ or ${\rm S}_7$ by a solvable group.
LA - eng
KW - non-solvable group; solvable group; character degree
UR - http://eudml.org/doc/297305
ER -
References
top- Benjamin, D., 10.1090/S0002-9939-97-04269-X, Proc. Am. Math. Soc. 125 (1997), 2831-2837. (1997) Zbl0889.20004MR1443370DOI10.1090/S0002-9939-97-04269-X
- Bianchi, M., Chillag, D., Lewis, M. L., Pacifici, E., 10.1090/S0002-9939-06-08651-5, Proc. Am. Math. Soc. 135 (2007), 671-676. (2007) Zbl1112.20006MR2262862DOI10.1090/S0002-9939-06-08651-5
- Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A., Wilson, R. A., Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups, Clarendon Press, Oxford (1985). (1985) Zbl0568.20001MR0827219
- Group, GAP, GAP -- Groups, Algorithms, and Programming. A System for Computational Discrete Algebra. Version 4.7.4, Available at http://www.gap-system.org (2014). (2014)
- Isaacs, I. M., 10.1090/chel/359, Pure and Applied Mathematics 69. Academic Press, New York (1976). (1976) Zbl0337.20005MR0460423DOI10.1090/chel/359
- Isaacs, I. M., Passman, D. S., 10.2140/pjm.1968.24.467, Pac. J. Math. 24 (1968), 467-510. (1968) Zbl0155.05502MR0241524DOI10.2140/pjm.1968.24.467
- James, G., Kerber, A., 10.1017/CBO9781107340732, Encyclopedia of Mathematics and Its Applications 16. Addison-Wesley, Reading (1981). (1981) Zbl0491.20010MR644144DOI10.1017/CBO9781107340732
- Manz, O., 10.1016/0021-8693(85)90210-8, J. Algebra 94 (1985), 211-255 German. (1985) Zbl0596.20007MR789547DOI10.1016/0021-8693(85)90210-8
- Manz, O., 10.1016/0021-8693(85)90042-0, J. Algebra 96 (1985), 114-119 German. (1985) Zbl0567.20004MR808844DOI10.1016/0021-8693(85)90042-0
- Schmid, P., 10.1016/S0021-8693(05)80060-2, J. Algebra 150 (1992), 254-256. (1992) Zbl0794.20022MR1174899DOI10.1016/S0021-8693(05)80060-2
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