Economical adjunction of square roots to groups
Dmitrii V. Baranov, Anton A. Klyachko
TL;DR
This paper investigates the minimal size of overgroups needed to contain square roots of all elements in a given group, providing near-optimal estimates and discussing related open questions.
Contribution
It offers an almost exact estimate for the minimal overgroup size required to contain square roots of all elements, improving understanding of group extensions.
Findings
Derived an estimate at most twice the optimal for overgroup size
Established bounds for the existence of square roots in group extensions
Presented open questions for further research
Abstract
How large must an overgroup of a given group be in order to contain a square root of any element of the initial group? We give an almost exact answer to this question (the obtained estimate is at most twice worse than the best possible) and state several related open questions.
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