Year: 2026
Type: preprint
Abstract: This PhD thesis studies the classification of group extensions, whose main result is the classification, up to isomorphism, of finite nonsolvable groups of order less than 23,040. To make this classification computationally effective, we develop reduction methods that replace extension computations involving a finite nonsolvable group by computations in suitable smaller solvable subgroups. This reduction from nonsolvable to solvable computations led to a major decrease in computing time and made it possible, on a standard personal computer available in 2002, to classify around 8.4 million nonsolvable groups of order less than 23,040. A nonsolvable group E is constructed from a given perfect kernel P, its perfect residual, extended by a given solvable quotient H=E/P. The isomorphism problem for the resulting nonsolvable groups E is reduced to isomorphism computations between extensions involving a small nilpotent subgroup U
Source: arXiv (Cornell University)
Author: Archer, Claude
Institution: Université Libre de Bruxelles
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1714713341