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Miklós Schweitzer 1961- Problem 1

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November 22, 2015
college contests

Problem Statement

1. Let aa ( ≠e\neq e, the unit element) be an element of finite order of a group GG and let tt (≥2\geq 2) be a positive integer. Show: if the complex A={e,a,a2,…,at−1}A= \{ e,a,a^2, \dots , a^{t-1} \} is not a group, then for every positive integer kk( 2≤k≤t2 \leq k \leq t) the complex B={e.ak,a2k,…,a(t−1)k}B= \{ e. a^k, a^{2k}, \dots , a^{(t-1)k} \} differs from AA. (A. 16)
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