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- W2963350415 abstract "This is a paper with two aims. First, we show that the map from $mathbb{Z}/pmathbb{Z}$ to itself defined by exponentiation $xto m^x$ has few $3$-cycles -- that is to say, the number of cycles of length three is $o(p)$. This improves on previous bounds. Our second objective is to contribute to an ongoing discussion on how to find a non-sofic group. In particular, we show that, if the Higman group were sofic, there would be a map from $mathbb{Z}/pmathbb{Z}$ to itself, locally like an exponential map, yet satisfying a recurrence property." @default.
- W2963350415 created "2019-07-30" @default.
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- W2963350415 date "2018-11-05" @default.
- W2963350415 modified "2023-09-24" @default.
- W2963350415 title "Soficity, short cycles, and the Higman group" @default.
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- W2963350415 doi "https://doi.org/10.1090/tran/7534" @default.
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