Lucchini, AndreaThakkar, Dhara2025-08-282025-08-282023-06-01http://arxiv.org/abs/2306.07633https://d8.irins.org/handle/IITG2025/19850Let G be a finite group. In order to determine the smallest cardinality d(G) of a generating set of G and a generating set with this cardinality, one should repeat many times the test whether a subset of G of small cardinality generates G. We prove that if a chief series of G is known, then the numbers of these generating tests can be drastically reduced. At most |G|13/5 subsets must be tested. This implies that the minimum generating set problem for a finite group G can be solved in polynomial time.en-USSmallest cardinalityCardinality generates Gpolynomial timeNPe-Printe-Print123456789/435