Counting conjugacy classes of cyclic subgroups for fusion systems

Thévenaz [6] made an interesting observation that the number of conjugacy classes of cyclic subgroups in a finite group G is equal to the rank of the matrix of the numbers of double cosets in G. We give another proof of this fact and present a fusion system version of it. In particular we use finite groups realizing the fusion system F as in our previous work [3].


Published in:
Journal of Group Theory, 17, 4, 661-666
Year:
2014
Publisher:
Berlin, Walter de Gruyter
ISSN:
1433-5883
Keywords:
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 Record created 2014-08-29, last modified 2018-03-17

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