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What is Subgroup Definition about?

A subgroup is a non-empty subset of a group that satisfies closure, contains the identity element, and includes inverses. The document provides examples, demonstrating that the set of all even integers is a subgroup of the integers under addition, while the set of positive even integers is not. It also discusses the properties of intersections and unions of subgroups, concluding that the intersection of subgroups is always a subgroup, while the union is a subgroup only if one is contained within the other.

Author

ftamlakgetu

Language

EN