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A group G is said to have a factorization if there exist proper subgroups $A$ and $B$ such that $G = AB = \{ ab \ | \ a \in A, b \in B \}$. The paper Factorisations of sporadic simple groups (...

The book The maximal factorizations of the finite simple groups and their automorphism groups (by Martin W. Liebeck, Cheryl E. Praeger and Jan Saxl) provides a classification of all the triples $(G,A,...

Let $G$ be a finite group and $\mathcal{L}(G)$ its subgroup lattice. Let $\mu$ be the Möbius function on $\mathcal{L}(G)$. The reduced Euler characteristic of the order complex of the coset poset $\{ ...

Let $[H,G]$ be a Boolean interval of finite groups (i.e. the lattice of intermediate subgroups $H \subseteq K \subseteq G$, is Boolean). For any element $K \in [H,G]$, let $K^{\complement}$ be its ...