The blocks with four irreducible characters
Suppose that $B$ is a Brauer $p$-block with defect group $D$. If $B$ exactly contains 4 irreducible characters, then we show that $D$ has order 4 or 5, assuming the Alperin--McKay conjecture.
math.GR↗
arXiv subjects
Lucía Sanus
Publications and source records attributed to Lucía Sanus.
Groups whose prime graph on class sizes has a cut vertex
Let $G$ be a finite group, and let $Δ(G)$ be the prime graph built on the set of conjugacy class sizes of $G$: this is the simple undirected graph whose vertices are the prime numbers dividing some conjugacy class size of $G$, two vertices $p$ and $q$ being adjacent if and only if $pq$ divides some conjugacy class size of $G$. In the present paper, we classify the finite groups $G$ for which $Δ(G)$ has a cut vertex.
math.GR↗