What question did this study set out to answer?

To determine the conditions under which a finite group is solvable based on the nilpotency probability.

June 19, 2026Open Access

Characterising Finite Solvable Groups Through the Nilpotency Probability

Puntos clave

To determine the conditions under which a finite group is solvable based on the nilpotency probability.
Analyzed the nilpotency probability of randomly chosen elements in finite groups.
Proved that if the nilpotency probability exceeds 1/12, the group is solvable.
Established a threshold for solvability: if ν(G) > 1/12, then G is solvable.

Resumen

Abstract Given a finite group G, we denote by ν (G) (G) nu left parenthesis upper G right parenthesis the probability that two randomly chosen elements of G generate a nilpotent subgroup. We prove that if ν (G) > 1 / 12, (G) > 1/12, nu left parenthesis upper G right parenthesis greater than 1 divided by 12 comma then G is solvable.

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Cite This Study

Andrea Lucchini (Mon,) studied this question.

synapsesocial.com/papers/6a34df2365a5b0777af2e449 https://doi.org/https://doi.org/10.1017/s0004972726101476

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