TL;DR
This paper explores the properties of Maximal Dimension (MaxDim), a group invariant related to subgroup configurations, proving additive behavior in certain cases and confirming a conjecture about group construction.
Contribution
It establishes conditions under which MaxDim behaves additively for product groups and proves a conjecture linking groups with smaller MaxDim to those with smaller i.
Findings
MaxDim(G×H) = MaxDim(G) + MaxDim(H) in specific cases
Confirmed Thieu's conjecture on constructing groups with smaller MaxDim
Provides insights into subgroup configuration behaviors
Abstract
In this paper, we investigate behaviors of Maximal Dimension, a group invariant involving certain configuration of maximal subgroups, which we denote by MaxDim. We prove that in some special cases, MaxDim(G\times H) = MaxDim(G) + MaxDim(H). We also prove a conjecture stated by Ellie Thieu which shows that groups with m < MaxDim can be constructed from groups with m < i.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicsgraph theory and CDMA systems · Finite Group Theory Research · Rings, Modules, and Algebras