|
This article is cited in 1 scientific paper (total in 1 paper)
On finite simple groups containing strongly isolated subgroups
N. D. Podufalov
Abstract:
Suppose that a finite simple group $G$ containing a strongly isolated subgroup whose order is divisible by $3$ has a $2$-local subgroup whose order is also divisible by $3$. Then $G$ is isomorphic either to $\operatorname{PSL}(3,4)$ or to $\operatorname{PSL}(2,q)$ for
a suitable $q$.
If a finite simple group $G$ contains for some prime number $p\in\{3,5\}\cap\pi(G)$ a strongly isolated subgroup whose order is divisible by $p$, then $G$ is isomorphic to one of the groups $\operatorname{PSL}(3,4)$, $\operatorname{PSL}(2,q)$ for a suitable $q$,
or $\operatorname{Sz}(2^{2m+1})$, $m>0$.
A number of other results on groups containing strongly isolated subgroups are also derived in the paper.
Bibliography: 13 titles.
Received: 18.06.1974 and 26.01.1976
Citation:
N. D. Podufalov, “On finite simple groups containing strongly isolated subgroups”, Mat. Sb. (N.S.), 100(142):3(7) (1976), 447–454; Math. USSR-Sb., 29:3 (1976), 403–409
Linking options:
https://www.mathnet.ru/eng/sm2865https://doi.org/10.1070/SM1976v029n03ABEH003676 https://www.mathnet.ru/eng/sm/v142/i3/p447
|
Statistics & downloads: |
Abstract page: | 216 | Russian version PDF: | 69 | English version PDF: | 8 | References: | 27 |
|