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Let $G$ be a finite group with a dicyclic subgroup $H$ . We show that if there exist $H$ -connected transversals in $G$ , then $G$ is a solvable group. We apply this result to loop theory and show that if the inner mapping group $I (Q)$ of a finite loop $Q$ is dicyclic, then $Q$ is a solvable loop. We also discuss a more general solvability criterion in the case where $I (Q)$ is a certain type of a direct product.

On diffeomorphisms over surfaces trivially embedded in the 4-sphere.

Hirose, Susumu (2002)

Algebraic & Geometric Topology

On dihedral 2-groups as inner mapping groups of finite commutative inverse property loops

Markku Niemenmaa (2018)

Commentationes Mathematicae Universitatis Carolinae

We show that finite commutative inverse property loops may not have nonabelian dihedral 2-groups as their inner mapping group.

On dimensions in Bredon homology.

Nucinkis, Brita E.A. (2004)

Homology, Homotopy and Applications

On Direct Decomposition of Torsion Free Abelian Groups.

Bjarni Jonsson (1959)

Mathematica Scandinavica

On direct decompositions of torsion-free abelian groups of finite rank

L. Fuchs, F. Loonstra (1970)

Rendiconti del Seminario Matematico della Università di Padova

On Direct Summands of A-Separable R-Modules.

Ulrich Albrecht (1990)

Forum mathematicum

On direct sums of $ℬ^{(1)}$ -groups

Claudia Metelli (1993)

Commentationes Mathematicae Universitatis Carolinae

A necessary and sufficient condition is given for the direct sum of two $ℬ^{(1)}$ -groups to be (quasi-isomorphic to) a $ℬ^{(1)}$ -group. A $ℬ^{(1)}$ -group is a torsionfree Abelian group that can be realized as the quotient of a finite direct sum of rank 1 groups modulo a pure subgroup of rank 1.

On direct sums of $B^{(1)}$ -groups – II

Clorinda De Vivo, Claudia Metelli (2006)

Commentationes Mathematicae Universitatis Carolinae

$B^{(1)}$ -groups are a class of torsionfree Abelian groups of finite rank, part of the main class of Butler groups. In the paper C. Metelli, On direct sums of $B^{(1)}$ -groups, Comment. Math. Univ. Carolinae 34 (1993), 587–591, the problem of direct sums of $B^{(1)}$ -groups was discussed, and a necessary and sufficient condition was given for the direct sum of two $B^{(1)}$ -groups to be a $B^{(1)}$ -group. While sufficiency holds, necessity was wrongly claimed; we solve here the problem, and in the process study a curious hierarchy among...

On disjoint covering of groups by their cosets

Ivan Korec, Štefan Znám (1977)

Mathematica Slovaca

On divisibility in definable groups

Margarita Otero (2009)

Fundamenta Mathematicae

Let ℳ be an o-minimal expansion of a real closed field. It is known that a definably connected abelian group is divisible. We show that a definably compact definably connected group is divisible.

On double coverings of some rotary hypermaps.

Breda, Ana, d'Azevedo, Antonio Breda, Catalano, Domenico (2009)

Beiträge zur Algebra und Geometrie

On Dual Semigroups

Dorota Krajňáková (1970)

Matematický časopis

On dual semigroups

Štefan Schwarz (1960)

Czechoslovak Mathematical Journal

On duality of submodule lattices

Gábor Czédli, Géza Takách (2000)

Discussiones Mathematicae - General Algebra and Applications

An elementary proof is given for Hutchinson's duality theorem, which states that if a lattice identity λ holds in all submodule lattices of modules over a ring R with unit element then so does the dual of λ.

On Dye's condition in nilpotent groups of class 2

Ernest Płonka (1974)

Colloquium Mathematicae

On Ek-semigroups.

A. Varisco, A. Cherubini (1986/1987)

Semigroup forum

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