2 problems

Let $G$ and $H$ be non-abelian finite groups. For a finite non-abelian group $K$, let $\Gamma_K$ be the graph whose vertices are the non-central elements of $K$, with two vertices…

Let $G$ and $H$ be finite abelian groups of the same order. Define the sum-of-element-orders function by … where $o(g)$ denotes the order of $g$. Tărnăuceanu's conjecture. The grou…