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Putnam 1975 B1

Source: Putnam 1975

February 17, 2022
Putnamgroup theoryabstract algebra

Problem Statement

Consider the additive group Z2\mathbb{Z}^{2}. Let HH be the smallest subgroup containing (3,8),(4,−1)(3,8), (4,-1) and (5,4)(5,4). Let HxyH_{xy} be the smallest subgroup containing (0,x)(0,x) and (1,y)(1,y). Find some pair (x,y)(x,y) with x>0x>0 such that H=HxyH=H_{xy}.
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