Assertion: abelian group's subgroup | /r/HasProperty | h of g
Facets:
Source sentences:
text: Lagrange's theorem states that for any subgroup H of G, the order of the subgroup divides the order of the group: |H| is a divisor of |G|.
text: Cosets are a basic tool in the study of groups; for example they play a central role in Lagrange's theorem that states that for any finite group G, the number of elements of every subgroup H of G divides the number of elements of G. Cosets of a particular type of subgroup (normal subgroup) can be used as the elements of another group called a quotient group or factor group.
text: If G is an abelian group, then g + H = H + g for every subgroup H of G and every element g of G.
text: and the subgroup H of G,
text: A discrete subgroup H of G is cocompact if there is a compact subset K of G