On the universality of words for the alternating groups
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- by Manfred Droste PDF
- Proc. Amer. Math. Soc. 96 (1986), 18-22 Request permission
Abstract:
We prove the following theorem on the finite alternating groups ${A_n}$: For each pair $(p,q)$ of nonzero integers there exists an integer $N(p,q)$ such that, for each $n \geqslant N$, any even permutation $a \in {A_n}$ can be written in the form $a = {b^p} \cdot {c^q}$ for some suitable elements $b,c \in {A_n}$. A similar result is shown to be true for the finite symmetric groups ${S_n}$ provided that $p$ or $q$ is odd.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 18-22
- MSC: Primary 20F10; Secondary 20B30, 20D06
- DOI: https://doi.org/10.1090/S0002-9939-1986-0813801-5
- MathSciNet review: 813801