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- Serial_subgroup abstract "In the mathematical field of group theory, a subgroup H of a given group G is a serial subgroup of G if there is a chain C of subgroups of G extending from H to G such that for consecutive subgroups X and Y in C, X is a normal subgroup of Y. The relation is written H ser G or H is serial in G.If the chain is finite between H and G, then H is a subnormal subgroup of G. Then every subnormal subgroup of G is serial. If the chain C is well-ordered and ascending, then H is an ascendant subgroup of G; if descending, then H is an descendant subgroup of G. If G is a locally finite group, then the set of all serial subgroups of G form a complete sublattice in the lattice of all normal subgroups of G.".
- Serial_subgroup wikiPageID "40735495".
- Serial_subgroup wikiPageRevisionID "576401654".
- Serial_subgroup subject Category:Subgroup_properties.
- Serial_subgroup comment "In the mathematical field of group theory, a subgroup H of a given group G is a serial subgroup of G if there is a chain C of subgroups of G extending from H to G such that for consecutive subgroups X and Y in C, X is a normal subgroup of Y. The relation is written H ser G or H is serial in G.If the chain is finite between H and G, then H is a subnormal subgroup of G. Then every subnormal subgroup of G is serial.".
- Serial_subgroup label "Serial subgroup".
- Serial_subgroup sameAs m.0y6jhjz.
- Serial_subgroup sameAs Q17096391.
- Serial_subgroup sameAs Q17096391.
- Serial_subgroup wasDerivedFrom Serial_subgroup?oldid=576401654.
- Serial_subgroup isPrimaryTopicOf Serial_subgroup.