The affine and projective groups are maximal
Itay Kaplan, Pierre Simon
TL;DR
This paper proves that the affine group AGL_n(Q) and the projective group PGL_n(Q) are maximal closed subgroups within the symmetric group S_infinity, highlighting their structural significance.
Contribution
It establishes the maximality of AGL_n(Q) and PGL_n(Q) as closed subgroups of S_infinity, a result not previously known.
Findings
AGL_n(Q) is a maximal closed subgroup of S_infinity
PGL_n(Q) is a maximal closed subgroup of S_infinity
These groups are structurally significant within the symmetric group
Abstract
We show that the groups AGL_n(Q) and PGL_n(Q), seen as closed subgroups of S_{\infty}, are maximal-closed.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Fuzzy and Soft Set Theory · Rings, Modules, and Algebras