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Subgroup

Basic definition

A subgroup is a subset of a mathematical group that is also a group.

Detailed definition

A subgroup is a subset H of group elements of a group G that satisfies the four group requirements. It must therefore contain the identity element. "H is a subgroup of G" is written H⊆G, or sometimes H<=G. The order of any subgroup of a group of order h must be a divisor of h. A subgroup H of a group G that does not include the entire group G itself is known as a proper subgroup, denoted H subset G or H<G.

Related terms

composition series | Fitting subgroup | group | normal subgroup | proper subgroup

Educational grade level

college level

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Volume of a Cylinder

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