Group automorphisms of incidence algebras.

Let (P,≤) be an arbitrary partially ordered set and I(P) its incidence space. Then FI(P) denotes the associated finitary incidence algebra, where FI(P) = I(P) for locally finite posets (P,≤). We investigate the group of units U(FI(P)) of incidence algebras and its normal subgroups. This includes the structure and properties of maximal abelian, normal subgroups, and criteria for solvability and nilpotency. Lastly, we will classify the automorphism group of the group of units when (P,≤) = (Z,≤).

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Doctoral

Grantor

Baylor University.

Year dc:date.issued

2021

Author dc:creator

• Rebrovich, Jack, 1994-

Advisor dc:contributor.advisor

• Herden, Daniel.

• Incidence algebras.
• Maximal abelian.
• Normal subgroups.

Statement dc:rights

• Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/2104/11583

OAI identifier oai:identifier

oai:baylor-ir.tdl.org:2104/11583