On two-generator subgroups in SL_2(Z), SL_2(Q), and SL_2(R)
Anastasiia Chorna, Katherine Geller, and Vladimir Shpilrain
TL;DR
This paper investigates the properties and membership problem complexities of parabolic Möbius subgroups within SL_2 over integers, rationals, and reals, providing insights into their algebraic structure and computational aspects.
Contribution
It analyzes the membership problem and algorithmic complexity for two-generator subgroups in SL_2 over Z, Q, and R, focusing on parabolic Möbius subgroups.
Findings
Characterized membership problem complexity for these subgroups
Developed algorithms for subgroup membership testing
Provided complexity bounds for the algorithms
Abstract
We consider what some authors call 'parabolic M\"obius subgroups' of matrices over Z, Q, and R and focus on the membership problem in these subgroups and complexity of relevant algorithms.
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · Holomorphic and Operator Theory