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Large Orbits of Supersolvable Linear Groups

✍ Scribed by Thomas R. Wolf

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
152 KB
Volume
215
Category
Article
ISSN
0021-8693

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✦ Synopsis

The study of regular orbits of linear groups plays an important role in representation theory, particularly that of solvable groups because a chief factor of a solvable group G is an irreducible G-module. If V is a Ε½ . G-module, recall that Β¨in V is in a regular orbit if C Β¨s 1, i.e., the G

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We prove that if an endomorphism Ο† of a free group F n of a finite rank n preserves an automorphic orbit Orb AutF n W with W = 1, i.e., if Ο† Orb AutF n W βŠ† Orb AutF n W , then Ο† is an automorphism.  2002 Elsevier Science (USA)