Central automorphisms of finite groups
1986 ◽
Vol 34
(2)
◽
pp. 191-198
◽
Keyword(s):
Group A
◽
This paper considers an aspect of the general problem of how the structure of a group influences the structure of its automorphisms group. A recent result of Beisiegel shows that if P is a p-group then the central automorphisms group of P has no normal subgroups of order prime to p. So, roughly speaking, most of the central automorphisms are of p-power order. This generalizes an old result of Hopkins that if Aut P is abelian (so every automorphisms is central), then Aut P is a p-group.This paper uses a different approach to consider the case when P is a π-group. It is shown that the central automorphism group of P has a normal. π′-subgroup only if P has an abelian direct factor whose automorphism group has such a subgroup.
1984 ◽
Vol 27
(1)
◽
pp. 59-60
2004 ◽
Vol 104
(2)
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pp. 223-229
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2006 ◽
Vol 106
(2)
◽
pp. 139-148
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2001 ◽
Vol 64
(3)
◽
pp. 565-575
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2006 ◽
Vol 106A
(2)
◽
pp. 139-148
2018 ◽
Vol 17
(02)
◽
pp. 1850026
2019 ◽
Vol 19
(09)
◽
pp. 2050167
Keyword(s):
2004 ◽
Vol 104A
(2)
◽
pp. 223-229
Keyword(s):