MathOverflow

Let $G$ be a finite group and $\phi : G \rightarrow G$ be a group automorphism such that for more than $\frac{3}{4}$ of elements $g \in G$ we have
$$\phi(g) = g^{-1}$$
Prove that for all $g \in G$

I'm trying to understand two different definitions of the cobar construction $\Omega C$ for a coaugmented dg coalgebra $C = \overline{C} \oplus \mathbb{k}$.
In Adams' original definition, $\Omega C$ is defined as the tensor algebra $T(s^{-1}\overline{C})$ with a differential which involves both the differential and coproduct of $C$. This definition has been well-studied in, for example, the book by Loday...

I have been studying approaches to the Riemann Hypothesis that use dynamical systems perspectives, particularly work connecting RH to random matrix theory and spectral analysis. I'm aware of:
The classical reformulations (Weil's explicit formula, various equivalent statements)Approaches using the von Koch bound ψ(x) - x = O(x^(1/2+ε))The role of the functional equation ζ(s) = ζ(1-s) in creating symmetryRecent work on RH via stability analysis...

I was idly thinking today about the functions $\displaystyle f(n) = \sum_{p \mid n} p$ and $\displaystyle F(n) = \sum_{p^e \| n} ep$, respectively the "sum of prime divisors" function and the "sum of prime divisors with multiplicity" function. These...