Some Remarks on Groups Admitting a Fixed-Point-Free Automorphism
1968 ◽
Vol 20
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pp. 1300-1307
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Keyword(s):
A finite group G is said to be a fixed-point-free-group (an FPF-group) if there exists an automorphism a which fixes only the identity element of G. The principal open question in connection with these groups is whether non-solvable FPF-groups exist. One of the results of the present paper is that if a Sylow p-group of the FPF-group G is the direct product of any number of mutually non-isomorphic cyclic groups, then G has a normal p-complement. As a consequence of this, the conjecture that all FPF-groups are solvable would be true if it were true that every finite simple group has a non-trivial SylowT subgroup of the kind just described. Here it should be noted that all the known simple groups satisfy this property.
2019 ◽
Vol 102
(1)
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pp. 77-90
Keyword(s):
2015 ◽
Vol 14
(04)
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pp. 1550056
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Keyword(s):
Keyword(s):
Keyword(s):
2016 ◽
Vol 09
(03)
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pp. 1650054
2019 ◽
Vol 18
(12)
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pp. 1950230
Keyword(s):
1998 ◽
Vol 58
(1)
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pp. 137-145
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Keyword(s):
2013 ◽
Vol 56
(1)
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pp. 221-227
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Keyword(s):
2009 ◽
Vol 19
(05)
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pp. 681-698
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