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In this short note, it is shown that if $A, B$ are $H$ -connected transversals for a finite subgroup $H$ of an infinite group $G$ such that the index of $H$ in $G$ is at least 3 and $H \cap H^{u} \cap H^{v} = 1$ whenever $u, v \in G ∖ H$ and $u v^{- 1} \in G ∖ H$ then $A = B$ is a normal abelian subgroup of $G$ .

Constructing Units in commutative group rings.

Klaus Hoechsmann (1992)

Manuscripta mathematica

Convex cocompact subgroups of mapping class groups.

Farb, Benson, Mosher, Lee (2002)

Geometry & Topology

Counting arithmetic subgroups and subgroup growth of virtually free groups

Amichai Eisenmann (2015)

Journal of the European Mathematical Society

Let $K$ be a $p$ -adic field, and let $H = P S L_{2} (K)$ endowed with the Haar measure determined by giving a maximal compact subgroup measure $1$ . Let $A L_{H} (x)$ denote the number of conjugacy classes of arithmetic lattices in $H$ with co-volume bounded by $x$ . We show that under the assumption that $K$ does not contain the element $ζ + ζ^{- 1}$ , where $ζ$ denotes the $p$ -th root of unity over $ℚ_{p}$ , we have $lim_{x \to \infty} \frac{log A L_{H} (x)}{x log x} = q - 1$ where $q$ denotes the order of the residue field of $K$ .

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Displaying 41 – 60 of 544

Centralizers of semisimple subgroups in locally finite simple groups

Certain normal subgroups of units in group rings.

Character theory of symmetric groups, analysis of long relators, and random walks.

Characterization of abelian-by-cyclic 3-rewritable groups

Characterization of Chernikov groups in the class of Shunkov groups with Sylow four-subgroups.

Characterizations of some types of $S F$ groups.

Classification of pro- $p$ subgroups of ${SL}_{2}$ over a $p$ -adic ring, where $p$ is an odd prime

Classification of Soluble Groups of Cohomologie Dimension Two.

Coherence of 3-manifold fundamental groups

Completely decomposable abelian groups any pure subgroup of which is completely decomposable

Conjugately dense subgroups in generalized FC-groups.

Conjugately dense subgroups of locally finite Chevalley groups of Lie rank 1.

Connected transversals -- the Zassenhaus case

Constructing Units in commutative group rings.

Convex cocompact subgroups of mapping class groups.

Counting arithmetic subgroups and subgroup growth of virtually free groups

Degree 1 and 2 representations of nilpotent groups and applications to units of group rings.

Descending Chains in Free Products.

Die harmonischen Involutionen der Permutationsgruppe P...L2 (K).

Divisibility properties of subgroup numbers for the modular group.

Currently displaying 41 – 60 of 544