3 problems

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Erdős's average-order conjecture for the iterated-totient height function
Erdős's average-order conjecture. The average order is
Conjectureopenadditive-functions average-order totient-functionarXiv posted 2 days ago
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The average-order solvability conjecture for finite groups
Let $G$ be a finite group, and let $\mathrm{o}(G)$ denote its average element order. Average-order solvability conjecture. If … then $G$ is solvable. The conjecture was proved by H…
Conjectureopenaverage-order finite-groupsarXiv posted 2 days ago
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The average-order characterization conjecture for $A_5$
Let $G$ be a finite group. Its average order is … where $o(x)$ denotes the order of $x$ . Average-order solvability conjecture. If … then $G$ is solvable. This conjecture gives a th…
Conjectureopenaverage-order finite-groups solvable-groupsarXiv posted 2 days ago

Erdős's average-order conjecture for the iterated-totient height function