Affiliation:
1. School of Mathematics and Statistics , 26463 Southwest University , Chongqing , 400715 , P. R. China
2. Department of Mathematics , Changshu Institute of Technology , Changshu , 215505 , P. R. China
Abstract
Abstract
Let 𝐺 be a 5-group of maximal class with major centralizer
G
1
=
C
G
(
G
2
/
G
4
)
G_{1}=C_{G}({G_{2}}/{G_{4}})
.
In this paper, we prove that the irreducible character degrees of a 5-group 𝐺 of maximal class are almost determined by the irreducible character degrees of the major centralizer
G
1
G_{1}
and show that the set of irreducible character degrees of a 5-group of maximal class is either
{
1
,
5
,
5
3
}
\{1,5,5^{3}\}
or
{
1
,
5
,
…
,
5
k
}
\{1,5,\ldots,5^{k}\}
with
k
≥
1
k\geq 1
.
Funder
National Natural Science Foundation of China
Fundamental Research Funds for the Central Universities
Natural Science Foundation of Jiangsu Province
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