%%visits: 5 ## introduction Lagrange’s Theorem for group
:= |G| = |H|i(H, G)
Corollaries of Lagrange’s Theorem.
If |G| is prime, then G has no subgroups
The order of a group generated by g, is k, then the k divides |G|
If |G| is prime, then G is a cyclic group. ## intuition
proof of Lagranges_theorem theorem uses cosets, mainly that they are
disjoint and collectively exhausting, so the order of the group (the
number of elements in it), are the number of cosets times the number of
elements in any given subgroup. ## rigour index of set H in group
:= i(H,G := The number of cosets of G with respect to H. ## exam clinic
## resources tags
:math:introduction_to_abstract_algebra:introduction_to_number_theory: