Generalization of a theorem of Bogolioùboff to topological groups. With an appendix on Banach mean values in nonabelian groups
Generalized Archimedean ideals
Generalized convolutions and delphic semigroups
Generators of categories of compact irreducible semigroups.
Geodesic loops.
Globality in semisimple Lie groups
In the first section of this paper we give a characterization of those closed convex cones (wedges) in the Lie algebra which are invariant under the maximal compact subgroup of the adjoint group and which are controllable in the associated simply connected Lie group , i.e., for which the subsemigroup generated by the exponential image of agrees with the whole group (Theorem 13). In Section 2 we develop some algebraic tools concerning real root decompositions with respect to compactly...
Green's relations on a compact semigroup
Group reflection and precompact paratopological groups
We construct a precompact completely regular paratopological Abelian group G of size (2ω)+ such that all subsets of G of cardinality ≤ 2ω are closed. This shows that Protasov’s theorem on non-closed discrete subsets of precompact topological groups cannot be extended to paratopological groups. We also prove that the group reflection of the product of an arbitrary family of paratopological (even semitopological) groups is topologically isomorphic to the product of the group reflections of the factors,...
Group representations in non-archimedean Banach spaces
Group structure in finite coverings of compact solenoidal groups.
Group Structures and Rectifiability in Powers of Spaces
We prove that if some power of a space X is rectifiable, then is rectifiable. It follows that no power of the Sorgenfrey line is a topological group and this answers a question of Arhangel’skiĭ. We also show that in Mal’tsev spaces of point-countable type, character and π-character coincide.
Groupoid -algebras.
Groupoids and compact quantum groups
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...
Gruppentopologien auf nichtabelschen abzählbaren Gruppen.