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Abstract
We prove that most permutations of degree n have some power which is a cycle of prime length approximately log n. Explicitly, we show that for n sufficiently large, the proportion of such elements is at least 1 − 5/log log n with the prime between log n and (log n)^{log} log ^{n}. The proportion of even permutations with this property is at least 1 − 7/log log n.
Original language  English 

Pages (fromto)  234246 
Number of pages  13 
Journal  Proceedings of the Edinburgh Mathematical Society 
Volume  64 
Issue number  2 
Early online date  24 May 2021 
DOIs  
Publication status  Published  May 2021 
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Dive into the research topics of 'Most permutations power to a cycle of small prime length'. Together they form a unique fingerprint.Projects
 1 Finished

Complexity of group algorithms and statistical fingerprints of groups
Praeger, C. & Niemeyer, A.
ARC Australian Research Council
21/02/19 → 31/12/22
Project: Research