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Coprime Automorphisms and Their Commutators

✍ Scribed by Christopher Parker; Martyn Quick

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
121 KB
Volume
244
Category
Article
ISSN
0021-8693

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πŸ“œ SIMILAR VOLUMES

Fixed Points of Coprime Automorphisms an
Fixed Points of Coprime Automorphisms and Generalizations of Glauberman's Z*-Theorem
✍ Paul Flavell; Geoffrey R. Robinson πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 65 KB

One of the most widely used applications of block theory to the U w x structure theory of finite groups is Glauberman's Z -theorem 2 , which asserts that if t is an involution of a finite group G which is not conjugate in G to any other involution of a Sylow 2-subgroup containing t, then Ε½ . Ε½ .

Right 2-Engel Elements and Commuting Aut
Right 2-Engel Elements and Commuting Automorphisms of Groups
✍ Marian Deaconescu; Gary L Walls πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 63 KB

It is shown that there is a close connection between the right 2-Engel elements of a group and the set of the so-called commuting automorphisms of the group. As a consequence, the following general theorem is proved: If G is a group and if Ε½ . R G denotes the subgroup of right 2-Engel elements, then

Automorphism groups with cyclic commutat
Automorphism groups with cyclic commutator subgroup and Hamilton cycles
✍ Edward Dobson; Heather Gavlas; Joy Morris; Dave Witte πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 670 KB

It has been shown that there is a Hamilton cycle in every connected Cayley graph on each group G whose commutator subgroup is cyclic of prime-power order. This paper considers connected, vertex-transitive graphs X of order at least 3 where the automorphism group of X contains a transitive subgroup G