Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the universality of words for the alternating groups

Author: Manfred Droste
Journal: Proc. Amer. Math. Soc. 96 (1986), 18-22
MSC: Primary 20F10; Secondary 20B30, 20D06
MathSciNet review: 813801
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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.

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Keywords: Alternating groups, finite symmetric group, permutation groups, universal words, conjugacy classes
Article copyright: © Copyright 1986 American Mathematical Society