Groups satisfying the two-prime hypothesis with a composition factor isomorphic to PSL 2 ( q ) for q ≥ 7

Mark L. Lewis; Yanjun Liu; Hung P. Tong-Viet

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 4, page 921-941
  • ISSN: 0011-4642

Abstract

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Let G be a finite group and write cd ( G ) for the degree set of the complex irreducible characters of G . The group G is said to satisfy the two-prime hypothesis if for any distinct degrees a , b ∈ cd ( G ) , the total number of (not necessarily different) primes of the greatest common divisor gcd ( a , b ) is at most 2 . We prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to PSL 2 ( q ) for q ≥ 7 .

How to cite

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Lewis, Mark L., Liu, Yanjun, and Tong-Viet, Hung P.. "Groups satisfying the two-prime hypothesis with a composition factor isomorphic to PSL$_2(q)$ for $q\ge 7$." Czechoslovak Mathematical Journal 68.4 (2018): 921-941. <http://eudml.org/doc/294463>.

@article{Lewis2018,
abstract = {Let $G$ be a finite group and write $\{\rm cd\} (G)$ for the degree set of the complex irreducible characters of $G$. The group $G$ is said to satisfy the two-prime hypothesis if for any distinct degrees $a, b \in \{\rm cd\} (G)$, the total number of (not necessarily different) primes of the greatest common divisor $\gcd (a, b)$ is at most $2$. We prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to PSL$_2 (q)$ for $q \ge 7$.},
author = {Lewis, Mark L., Liu, Yanjun, Tong-Viet, Hung P.},
journal = {Czechoslovak Mathematical Journal},
keywords = {character degrees; prime divisors},
language = {eng},
number = {4},
pages = {921-941},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Groups satisfying the two-prime hypothesis with a composition factor isomorphic to PSL$_2(q)$ for $q\ge 7$},
url = {http://eudml.org/doc/294463},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Lewis, Mark L.
AU - Liu, Yanjun
AU - Tong-Viet, Hung P.
TI - Groups satisfying the two-prime hypothesis with a composition factor isomorphic to PSL$_2(q)$ for $q\ge 7$
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 4
SP - 921
EP - 941
AB - Let $G$ be a finite group and write ${\rm cd} (G)$ for the degree set of the complex irreducible characters of $G$. The group $G$ is said to satisfy the two-prime hypothesis if for any distinct degrees $a, b \in {\rm cd} (G)$, the total number of (not necessarily different) primes of the greatest common divisor $\gcd (a, b)$ is at most $2$. We prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to PSL$_2 (q)$ for $q \ge 7$.
LA - eng
KW - character degrees; prime divisors
UR - http://eudml.org/doc/294463
ER -

References

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  8. Isaacs, I. M., 10.2307/2373731, Am. J. Math. 95 (1973), 594-635. (1973) Zbl0277.20008MR0332945DOI10.2307/2373731
  9. Isaacs, I. M., Character Theory of Finite Groups, Pure and Applied Mathematics 69. Academic Press, New York (1976). (1976) Zbl0337.20005MR0460423
  10. Lewis, M. L., Liu, Y., 10.1007/s00605-015-0839-z, Monatsh. Math. 181 (2016), 855-867. (2016) Zbl06655173MR3563303DOI10.1007/s00605-015-0839-z
  11. Lewis, M. L., Liu, Y., Tong-Viet, H. P., 10.1007/s00605-016-0954-5, Monatsh. Math. 184 (2017), 115-131. (2017) Zbl1378.20009MR3683947DOI10.1007/s00605-016-0954-5
  12. White, D. L., 10.1515/jgt-2012-0026, J. Group Theory 16 (2013), 1-33. (2013) Zbl1294.20014MR3008309DOI10.1515/jgt-2012-0026

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