Monolithic group: Difference between revisions
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===Symbol-free definition=== | ===Symbol-free definition=== | ||
A [[group]] is said to be '''monolithic''' if it has a unique [[defining ingredient::minimal normal subgroup]], and this is contained in ''every'' nontrivial [[defining ingredient::normal subgroup]] | A [[group]] is said to be '''monolithic''' if it has a unique [[defining ingredient::minimal normal subgroup]], and this is contained in ''every'' nontrivial [[defining ingredient::normal subgroup]]. This minimal normal subgroup is termed a '''monolith'''. | ||
==Relation with other properties== | ==Relation with other properties== | ||
Revision as of 16:38, 30 August 2008
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
This is a variation of simplicity|Find other variations of simplicity | Read a survey article on varying simplicity
Definition
Symbol-free definition
A group is said to be monolithic if it has a unique minimal normal subgroup, and this is contained in every nontrivial normal subgroup. This minimal normal subgroup is termed a monolith.