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math.GR2026
Commuting probability of skew left braces
Susanta Mondal, Manoj K. Yadav
We introduce a concept of the commuting probability of a skew left brace analogous to group theory. We establish upper and lower bounds for the commuting probability and prove that…
math.GR2026
Skew brace extensions, second cohomology and complements
Nishant Rathee, Manoj K. Yadav
We study extensions and second cohomology of skew left braces via the natural semi-direct products associated with the skew left braces. Let be a skew b…