Article contents
NONDIVISIBILITY AMONG IRREDUCIBLE CHARACTER CO-DEGREES
Published online by Cambridge University Press: 24 May 2021
Abstract
For a character
$\chi $
of a finite group G, the number
$\chi ^c(1)={[G:{\textrm {ker}}\chi ]}/{\chi (1)}$
is called the co-degree of
$\chi $
. A finite group G is an
${\textrm {NDAC}} $
-group (no divisibility among co-degrees) when
$\chi ^c(1) \nmid \phi ^c(1)$
for all irreducible characters
$\chi $
and
$\phi $
of G with
$1< \chi ^c(1) < \phi ^c(1)$
. We study finite groups admitting an irreducible character whose co-degree is a given prime p and finite nonsolvable
${\textrm {NDAC}} $
-groups. Then we show that the finite simple groups
$^2B_2(2^{2f+1})$
, where
$f\geq 1$
,
$\mbox {PSL}_3(4)$
,
${\textrm {Alt}}_7$
and
$J_1$
are determined uniquely by the set of their irreducible character co-degrees.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 105 , Issue 1 , February 2022 , pp. 68 - 74
- Copyright
- © 2021 Australian Mathematical Publishing Association Inc.
References
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