Transfinite normal and composition series of groups
Ruslan Sharipov
TL;DR
This paper investigates the properties of normal and composition series of groups indexed by ordinal numbers, establishing a Jordan-Holder theorem for these transfinite series.
Contribution
It introduces a framework for transfinite series of groups and proves a Jordan-Holder theorem extending classical results to this broader context.
Findings
Established the Jordan-Holder theorem for transfinite series
Extended the theory of group series to ordinal-indexed cases
Provided foundational results for transfinite group decompositions
Abstract
Normal and composition series of groups enumerated by ordinal numbers are studied. The Jordan-Holder theorem for them is proved.
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Taxonomy
TopicsFunctional Equations Stability Results · Advanced Topology and Set Theory · Advanced Topics in Algebra