Finite Groups Whose Character Graphs Associated with Codegrees Have No Triangles

Some finite groups with divisibility graph containing no triangles

Let $G$ be a finite group. The graph $D(G)$ is a divisibility graph of $G$. Its vertex set is the non-central conjugacy class sizes of $G$ and there is an edge between vertices $a$ and $b$ if and only if $a|b$ or $b|a$. In this paper, we investigate the structure of the divisibility graph $D(G)$ for a non-solvable group with $sigma^{ast}(G)=2$, a finite simple group $G$ that satisfies the one-p...

Solvable groups whose character degree graphs have non-trivial fundamental groups

In this talk, we introduce the character degree graph of a finite group G. We will discuss various properties of this graph, and we will further discuss what graphs can occur as the character degree graphs of finite solvable groups. In particular, we focus on groups with characters of degree pq, pr, and qr, where p, q, and r are distinct primes. Although some group theory will be assumed, knowl...

Finite p-groups with few non-linear irreducible character kernels

Abstract. In this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.

On Finite Groups With Two Irreducible Character Degrees

Polygons Whose Vertex Triangles Have Equal Area