The universality of words $x^ ry^ s$ in alternating groups
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- by J. L. Brenner, R. J. Evans and D. M. Silberger PDF
- Proc. Amer. Math. Soc. 96 (1986), 23-28 Request permission
Abstract:
If $r,s$ are nonzero integers and $m$ is the largest squarefree divisor of $rs$, then for every element $z$ in the alternating group ${A_n}$, the equation $z = {x^r}{y^s}$ has a solution with $x,y \in {A_n}$, provided that $n \geqslant 5$ and $n \geqslant (5/2)\log m$. The bound $(5/2)\log m$ improves the bound $4m + 1$ of Droste. If $n \geqslant 29$, the coefficient $5/2$ may be replaced by 2; however, $5/2$ cannot be replaced by 1 even for all large $n$.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 23-28
- MSC: Primary 20F10; Secondary 20B35
- DOI: https://doi.org/10.1090/S0002-9939-1986-0813802-7
- MathSciNet review: 813802