Subgroup • Lutalli

PROP-SG-A.

Let $G$ be a group and $H\subseteq G$ be non-empty. $H$ is a subgroup as soon as

$ab\in H$ for all $a$, $b\in H$;

$a^{-1}\in H$ for all $a\in H$.

PROP-SG-B.

Let $G$ be a group and $H\subseteq G$ be non-empty. $H$ is a subgroup as soon as
\[ab^{-1}\in H\]
for all $a$, $b\in H$.

PROP-SG-C.

Let $G$ be a finite group and $H\subseteq G$ be non-empty. $H$ is a subgroup as soon as
\[ab\in H\]
for all $a$, $b\in H$.