Affiliation:
1. Department of Mathematics , Shanghai University , Shanghai 200444 , P. R. China
Abstract
Abstract
Let A be an elementary abelian r-group acting on a finite
r
′
{r^{\prime}}
-group G. Suppose that the fixed-point group
C
G
(
a
)
{\operatorname{C}_{G}(a)}
is supersolvable for each
a
∈
A
#
{a\in A^{\#}}
. We show that G is supersolvable if
|
A
|
⩾
r
4
{|A|\geqslant r^{4}}
and that
G
′
⩽
𝐅
3
(
G
)
{G^{\prime}\leqslant\mathbf{F}_{3}(G)}
if
|
A
|
⩾
r
3
{|A|\geqslant r^{3}}
. Moreover, we prove some other results for cases when the fixed-point group
C
G
(
a
)
{\operatorname{C}_{G}(a)}
is abelian, p-nilpotent or satisfies the Sylow tower property.
Funder
National Natural Science Foundation of China
Subject
Algebra and Number Theory
Cited by
1 articles.
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