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- W3013930408 abstract "In recent work, Pomerance and Shparlinski have obtained results on the number of cycles in the functional graph of the map $x mapsto x^a$ in $mathbb{F}_p^*$. We prove similar results for other families of finite groups. In particular, we obtain estimates for the number of cycles for cyclic groups, symmetric groups, dihedral groups and $SL_2(mathbb{F}_q)$. We also show that the cyclic group of order $n$ minimizes the number of cycles among all nilpotent groups of order $n$ for a fixed exponent. Finally, we pose several problems." @default.
- W3013930408 created "2020-04-03" @default.
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- W3013930408 date "2017-07-20" @default.
- W3013930408 modified "2023-09-26" @default.
- W3013930408 title "Power maps in finite groups" @default.
- W3013930408 hasPublicationYear "2017" @default.
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