Year: 2025
Type: article
Abstract: A class $$\mathcal {S}$$ S of soluble groups is D-bounded when there exists a uniform upper bound for the lengths $$d(\varGamma )$$ d ( Γ ) of the derived series for $$\varGamma \in \mathcal {S}$$ Γ ∈ S . A theorem of Zassenhaus (Abh. Math. Semin. Hansisch. Univ. 12 , 289–312, 1938) states that for each n the class of soluble subgroups of $$GL(n,\mathbb {C})$$ G L ( n , C ) is D -bounded. Although Zassenhaus’s theorem is fundamental to the study infinite discrete linear groups the proof given here is located within the theory of continuous groups and the only discrete groups which appear are finite.
Source: Vietnam Journal of Mathematics
Author: F. E. A. Johnson
Institution: University College London
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4410380488