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## Main Question or Discussion Point

because the only thing the definition asks to check is the closure and inverse axioms?

this arose from a problem I was working on. elements with infinite order of an abelian grp G do not necessarly make a subgrp with 0. counter example: Z x Z3

consider (1,1),(-1,1) both with inf. order but their sum (0,2) has order 3.

sorry for the abbrev. I am sending this from my phone

this arose from a problem I was working on. elements with infinite order of an abelian grp G do not necessarly make a subgrp with 0. counter example: Z x Z3

consider (1,1),(-1,1) both with inf. order but their sum (0,2) has order 3.

sorry for the abbrev. I am sending this from my phone