Let $A$ be a given nonempty set. $S(A)$ is a group with respect to mapping composition. For a fixed element $a$ in $A$, let $H_{a}$ denote the set of all $f \in S(A)$ such that $f(a) = a$. Prove that $H_{a}$ is a subgroup of $S(A)$.
subgroup problem in abstract algebra
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abstract-algebra
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5I don't suppose you have any thoughts of your own? – 2012-04-08
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3You haven't said what $S(A)$ is. What have you tried? Do you know how to check whether something is a subgroup? For example, you have to check that a product of two elements of $H_a$ is in $H_a$. What does that mean? – 2012-04-08
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0Sorry. Let $S(A)$ denote the set of all permutations on $A$ – 2012-04-09