Groupoids and the associative law XII. (Representable cardinal functions)
Groupoids and the Brauer group
Groupoids assigned to relational systems
By a relational system we mean a couple where is a set and is a binary relation on , i.e. . To every directed relational system we assign a groupoid on the same base set where if and only if . We characterize basic properties of by means of identities satisfied by and show how homomorphisms between those groupoids are related to certain homomorphisms of relational systems.
Groupoids, stability cokernel sequences and duality
Groupoids, the Phragmen-Brouwer property, and the Jordan curve theorem.
Groupoids with a closure condition
Groupoids with non-associative triples on the diagonal
Groups acting on cube complexes.
Groups acting on products of trees, tiling systems and analytic -theory.
Groups acting on trees : from local to global structure
Groups – Additive Notation
We translate the articles covering group theory already available in the Mizar Mathematical Library from multiplicative into additive notation. We adapt the works of Wojciech A. Trybulec [41, 42, 43] and Artur Korniłowicz [25]. In particular, these authors have defined the notions of group, abelian group, power of an element of a group, order of a group and order of an element, subgroup, coset of a subgroup, index of a subgroup, conjugation, normal subgroup, topological group, dense subset and basis...
Groups All of Whose Subgroups are M-Groups.
Groups all whose nonnormal subgroups generate a nontrivial proper subgroup.
Groups as the union of proper subgroups.
Groups generated by k-root subgroups.
Groups generated by k-transvections.
Groups generated by positive multi-twists and the fake lantern problem.
Groups generated by two mutually Engel periodic elements
Scriviamo ed . Cerchiamo gruppi con generatori tali che ed per alcuni numeri naturali , .
Groups in which certain equations have many solutions
Groups in which -maximal subgroups are dualpronormal