Let $S(\mathbb N)$ be the set of all bijections on $\mathbb N$ ( the set of positive integers ) endowed with the natural group structure of function composition . If $H$ is a normal subgroup of $S(\mathbb N)$ such that $H$ contains an element of infinite order then is it true that $H=S(\mathbb N)$ ?
2026-03-26 06:31:44.1774506704
$H$ is a normal subgroup (containing an element of infinite order) of the permutation group over positive integers , then is $H$ the whole group?
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