If $G$ is a group and $H$ is subgroup of $G$, can I mark like this: $$K\prec G\;\;$$
Or I need to do this $$K<G\;\;$$
Thank you!
$\endgroup$ 33 Answers
$\begingroup$I usually go with the second symbol. Note that there $<$ is used if $K$ is a proper subgroup of $G$. Otherwise $\leq$ can be used.
$\endgroup$ $\begingroup$I noticed that the most used for a proper subgroup is the symbol $<$, otherwise $\leq$. If you see $H \triangleleft G$, it means $H$ is a normal subgroup of $G$. The expression $L_1 \prec L_2$ is used to show that $L_1$ is Karp reducible to $L_2$.
$\endgroup$ $\begingroup$It depends. If H is a subgroup of G, and is not equal to G, then use $<$, otherwise use $\leq$.
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