Doctoral Dissertations

Keywords and Phrases

group theory; magic group; magic square; triangular group

Abstract

In this research, we discuss two new topics in group theory. First, we define an n-magic square in a group to be a nxn array of group elements whose rows, columns, and diagonals have the same product. This definition is akin to the idea of magic squares in the integers. Groups that have an n-magic square are said to be n-magic. We begin with some preliminary results and focus much of our attention on 3-magic groups, though we also give some results for higher n. Through a series of propositions, we ultimately prove a characterization theorem for 3-magic finitely generated abelian groups and later show that all odd nonabelian groups are 3-magic. We also define an n-triangle in a group to be a triangle formed by n rows of group elements in which each element is the product of the two elements below it. We call a group that exhibits an n-triangle to be n-triangular and the largest n for which a group G is n-triangular is defined to be T(G). We give many preliminary results and characterize the 3-triangular abelian groups. We also give some results relating to higher n. This research concludes with an appendix of the 3-magicness of all even nonabelian groups up to order 50 and some findings on T(G) for all groups up to order 50.

Advisor(s)

Insall, Matt

Committee Member(s)

Grow, David E.
Wunsch, Donald C.
Murphy, Jason
Singler, John R.

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

Missouri University of Science and Technology

Publication Date

Summer 2025

Pagination

iv, 84 pages

Note about bibliography

Includes_bibliographical_references_(page 81)

Rights

© 2025 Nicholas Charles Fleece , All Rights Reserved

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 12536

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Included in

Mathematics Commons

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