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n-Dimensional Linear Representations of Aut Fn, and More

โœ Scribed by Andrei S. Rapinchuk


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
155 KB
Volume
197
Category
Article
ISSN
0021-8693

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We study the maximum order of torsion elements in GL n, Z and Aut F , n ลฝ . ลฝ . ลฝ . denoted G n and H n , respectively. We prove a Landau-type estimate log G n ; ลฝ . ลฝ . n log n , and we show that H n s G n if and only if n / 2, 6, 12. แฎŠ 1998 ' Academic Press

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If G is a group, H a subgroup of G, and โ€ a transitive G-set we ask under what ลฝ < <. conditions one can guarantee that H has a regular orbit s of size H on โ€. ลฝ . ลฝ . Here we prove that if PSL n, q : G : PGL n, q and H is cyclic then H has a ลฝ . regular orbit in every non-trivial G-set with few ex