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Finite groups acting on surfaces and the genus of a group

โœ Scribed by Thomas W Tucker


Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
1015 KB
Volume
34
Category
Article
ISSN
0095-8956

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โœ Ryoji Kasagawa ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 184 KB

We study representations of subgroups of the mapping class group M g of a surface of genus g 2 arising from the actions of them on the first cohomology groups of the surface with local coefficient systems which are defined by nontrivial homomorphisms ฯ€ 1 (ฮฃ g , \* ) โ†’ Z 2 = Aut(Z). As an application

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โœ Thomas W. Tucker ๐Ÿ“‚ Article ๐Ÿ“… 1981 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 115 KB ๐Ÿ‘ 1 views

## Abstract This Note announces two results on the genus of a group. First, there is exactly one group of genus two, thus answering a question of V. K. Proulx. Second, the genus of the full symmetric group of degree __n__ is __n__!/168 + 1, for all __n__ > 167.