Finite Groups Which are Automorphism Groups of Infinite Groups Only
Keyword(s):
AbstractThe object of this paper is to exhibit an infinite set of finite semisimple groups H, each of which is the automorphism group of some infinite group, but of no finite group. We begin the construction by choosing a finite simple group S whose outer automorphism group and Schur multiplier possess certain specified properties. The group H is a certain subgroup of Aut S which contains S. For example, most of the PSL's over a non-prime finite field are candidates for S, and in this case, H is generated by all of the inner, diagonal and graph automorphisms of S.
1983 ◽
Vol 26
(3)
◽
pp. 297-306
◽
Keyword(s):
Keyword(s):
1969 ◽
Vol 10
(1-2)
◽
pp. 162-168
◽
Keyword(s):
1986 ◽
Vol 40
(2)
◽
pp. 253-260
◽
Keyword(s):
1995 ◽
Vol 118
(2)
◽
pp. 207-213
◽
1978 ◽
Vol 25
(1)
◽
pp. 19-24
◽
Keyword(s):
2018 ◽
Vol 17
(07)
◽
pp. 1850122
◽
1989 ◽
Vol 106
(3)
◽
pp. 385-388
◽