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Full-Text Articles in Other Mathematics
The Root Finite Condition On Groups And Its Application To Group Rings, James Gollin
The Root Finite Condition On Groups And Its Application To Group Rings, James Gollin
Theses and Dissertations
A group $G$ is said to satisfy the root-finite condition if for every $g \in G$, there are only finitely many $x \in G$ such that there exists a positive integer $n$ such that $x^n = g$. It is shown that groups satisfy the root-finite condition iff they satisfy three subconditions, which are shown to be independent. Free groups are root-finite. Ordered groups are shown to satisfy one of the subconditions for the root-finite condition. Finitely generated abelian groups satisfy the root-finite condition. If, in a torsion-free abelian group $G$, there exists a positive integer $r$ such that the subgroup …
The Automorphism Group Of The Halved Cube, Benjamin B. Mackinnon
The Automorphism Group Of The Halved Cube, Benjamin B. Mackinnon
Theses and Dissertations
An n-dimensional halved cube is a graph whose vertices are the binary strings of length n, where two vertices are adjacent if and only if they differ in exactly two positions. It can be regarded as the graph whose vertex set is one partite set of the n-dimensional hypercube, with an edge joining vertices at hamming distance two. In this thesis we compute the automorphism groups of the halved cubes by embedding them in R n and realizing the automorphism group as a subgroup of GLn(R). As an application we show that a halved cube is a circulant graph if …