Abstract
AbstractLet p be an odd prime and G be a finite group with $$O_{p'}(G)=1$$
O
p
′
(
G
)
=
1
of p-rank at most 2 that contains an isolated element of order p. If $$x\notin Z(G)$$
x
∉
Z
(
G
)
, we show that $$F^*(G)$$
F
∗
(
G
)
is simple and we describe the structure of a Sylow p-subgroup P of $$F^*(G)$$
F
∗
(
G
)
as well as the fusion system $$\mathcal F_P(F^*(G))$$
F
P
(
F
∗
(
G
)
)
without using the classification of finite simple groups.
Funder
Martin-Luther-Universität Halle-Wittenberg
Publisher
Springer Science and Business Media LLC