What does the notation $H=\{ a | a^2=e \}$ mean?

Question

What is the meaning of notation $H=\{ a | a^2=e \}$? Is it the same as $H=\{a,a^2=e\}$?

(Here $a$ is an element of some group, with identity $e$.)

Answer 1

I can't see what you mean by $H=\{a,a^2=e\}$. In any case, the notation $H=\{a\mid a^2=e\}$ means the following (here I am assuming that $H$ is supposed to be a subset of some bigger set $X$, otherwise it makes no sense):

"H is the set containing all the elements $a\in X$ such that $a^2 = e$"

E.g., if $X=\mathbb R$ and $e$ denotes the identity element $e=1$, we will have that $H=\{-1,1\}$.

Edit: typo.