TL;DR
This paper introduces new, longer nilpotent series that provide a more detailed understanding of the structure of automorphisms in nilpotent groups, with applications to group-isomorphism testing.
Contribution
It presents a method to generate arbitrarily longer nilpotent series that refine existing series, enhancing structural analysis of nilpotent groups.
Findings
New nilpotent series can be arbitrarily longer than traditional series
Refined series clarify automorphism structures
Application demonstrated in group-isomorphism testing
Abstract
New nilpotent series are produced that refine the usual nilpotent series of a group. These refinements can be arbitrarily longer than the series they refine and therefore clarify in greater detail the structure of automorphisms of nilpotent groups. Examples, properties, and an application to group-isomorphism testing are provided.
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Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · Geometric and Algebraic Topology