Subgroup S-commutativity degrees of finite groups
Copyright policy )Subgroup S-commutativity degrees of finite groups
The so--called subgroup commutativity degree $sd(G)$ of a finite group $G$ is the number of permuting subgroups $(H,K) \in \mathrm{L}(G) \times \mathrm{L}(G)$, where $\mathrm{L}(G)$ is the subgroup lattice of $G$, divided by $|\mathrm{L}(G)|^2$. It allows us to measure how $G$ is far from the celebrated classification of quasihamiltonian groups of K. Iwasawa. Here we generalize $sd(G)$, looking at suitable sublattices of $\mathrm{L}(G)$, and show some new lower bounds.
8 pages; to appear in Bull. Belgian Math. Soc. with revisions
- University of Camerino Italy
- University of Palermo Italy
- University of Paris-Saclay France
Subgroup commutativity degrees, modular groups, Möbius number, abelian groups, Group Theory (math.GR), 20D60, permutability degree, Möbius numbers, Probabilistic methods in group theory, FOS: Mathematics, Mathematics - Combinatorics, subgroup commutativity degrees, maximal subgroups, Arithmetic and combinatorial problems involving abstract finite groups, Subnormal subgroups of abstract finite groups, numbers of permuting subgroups, Subgroups lattice; modular groups; permutability degree, sublattices, 20D60, 06B23, Series and lattices of subgroups, subgroup lattices, finite groups, lattices of subnormal subgroups, Subgroups lattice, Products of subgroups of abstract finite groups, 06B23, commutativity degrees, Combinatorics (math.CO), Mathematics - Group Theory
Subgroup commutativity degrees, modular groups, Möbius number, abelian groups, Group Theory (math.GR), 20D60, permutability degree, Möbius numbers, Probabilistic methods in group theory, FOS: Mathematics, Mathematics - Combinatorics, subgroup commutativity degrees, maximal subgroups, Arithmetic and combinatorial problems involving abstract finite groups, Subnormal subgroups of abstract finite groups, numbers of permuting subgroups, Subgroups lattice; modular groups; permutability degree, sublattices, 20D60, 06B23, Series and lattices of subgroups, subgroup lattices, finite groups, lattices of subnormal subgroups, Subgroups lattice, Products of subgroups of abstract finite groups, 06B23, commutativity degrees, Combinatorics (math.CO), Mathematics - Group Theory
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