The minimum generating set problem

Andrea Lucchini,Dhara Thakkar

doi:10.1016/j.jalgebra.2023.11.012

The minimum generating set problem

Andrea Lucchini, Dhara Thakkar

Open Access

https://doi.org/10.1016/j.jalgebra.2023.11.012

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Journal: Journal of Algebra	Publication Date: Nov 20, 2023
License type: cc-by

Affiliation: Indian Institute of Technology Gandhinagar, University of Padua

#Finite Group #Polynomial Time + Show 2 more

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Abstract

Let 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.

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