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- Maximal_subgroup abstract "In mathematics, the term maximal subgroup is used to mean slightly different things in different areas of algebra.In group theory, a maximal subgroup H of a group G is a proper subgroup, such that no proper subgroup K contains H strictly. In other words H is a maximal element of the partially ordered set of proper subgroups of G. Maximal subgroups are of interest because of their direct connection with primitive permutation representations of G. They are also much studied for the purposes of finite group theory: see for example Frattini subgroup, the intersection of the maximal subgroups.In semigroup theory, a maximal subgroup of a semigroup S is a subgroup (that is, a subsemigroup which forms a group under the semigroup operation) of S which is not properly contained in another subgroup of S. Notice that, here, there is no requirement that the maximal subgroup be proper, so if S is in fact a group then its unique maximal subgroup (as a semigroup) is S itself. Considering subgroups, and in particular maximal subgroups, of semigroups often allows one to apply group-theoretic techniques in semigroup theory. There is a one-to-one correspondence between idempotent elements of a semigroup and maximal subgroups of the semigroup: each idempotent element is the identity element of a unique maximal subgroup.".
- Maximal_subgroup wikiPageID "1472649".
- Maximal_subgroup wikiPageRevisionID "572110755".
- Maximal_subgroup hasPhotoCollection Maximal_subgroup.
- Maximal_subgroup subject Category:Group_theory.
- Maximal_subgroup subject Category:Subgroup_properties.
- Maximal_subgroup type Abstraction100002137.
- Maximal_subgroup type Possession100032613.
- Maximal_subgroup type Property113244109.
- Maximal_subgroup type Relation100031921.
- Maximal_subgroup type SubgroupProperties.
- Maximal_subgroup comment "In mathematics, the term maximal subgroup is used to mean slightly different things in different areas of algebra.In group theory, a maximal subgroup H of a group G is a proper subgroup, such that no proper subgroup K contains H strictly. In other words H is a maximal element of the partially ordered set of proper subgroups of G. Maximal subgroups are of interest because of their direct connection with primitive permutation representations of G.".
- Maximal_subgroup label "Maximal subgroup".
- Maximal_subgroup sameAs Maximale_Untergruppe.
- Maximal_subgroup sameAs m.054764.
- Maximal_subgroup sameAs Q16908484.
- Maximal_subgroup sameAs Q16908484.
- Maximal_subgroup sameAs Maximal_subgroup.
- Maximal_subgroup wasDerivedFrom Maximal_subgroup?oldid=572110755.
- Maximal_subgroup isPrimaryTopicOf Maximal_subgroup.