I have a question regarding notation in modular arithmetic and congruence classes.
I am used to the notation $a \equiv b$ $(\mod n)$; it simply means n divides a-b
But I've seen a similar notation in the context of groups (old fashioned one I believe) where the n is replaced by a subgroup and that got me slightly confused. Here it is:
If G is a group, a,b elements in G and P a subgroup of G, then what is the exact meaning of
$a \equiv b$ $(\mod P)$ ? Is it equivalent to $ap_1$=$bp_2$ for some $p_1$,$p_2$ in P?
