Groups of p-rank 2 containing an isolated element of order p
Let p be an odd prime and G be a finite group with O p ′ ( G ) = 1 of p -rank at most 2 that contains an isolated element of order p . If x ∉ Z ( G ) , we show that F ∗ ( G ) is simple and we describe the structure of a Sylow p -subgroup P of F ∗ ( G ) as well as the fusion system F P ( F ∗ ( G ) )...
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Published in | Archiv der Mathematik Vol. 118; no. 4; pp. 349 - 359 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Cham
Springer International Publishing
2022
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | Let
p
be an odd prime and
G
be a finite group with
O
p
′
(
G
)
=
1
of
p
-rank at most 2 that contains an isolated element of order
p
. If
x
∉
Z
(
G
)
, we show that
F
∗
(
G
)
is simple and we describe the structure of a Sylow
p
-subgroup
P
of
F
∗
(
G
)
as well as the fusion system
F
P
(
F
∗
(
G
)
)
without using the classification of finite simple groups. |
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ISSN: | 0003-889X 1420-8938 |
DOI: | 10.1007/s00013-022-01703-7 |