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On geometric convergence of discrete groups

Shihai Yang (2014)

Czechoslovak Mathematical Journal

One of the basic questions in the Kleinian group theory is to understand both algebraic and geometric limiting behavior of sequences of discrete subgroups. In this paper we consider the geometric convergence in the setting of the isometric group of the real or complex hyperbolic space. It is known that if Γ is a non-elementary finitely generated group and ρ i : Γ → SO ( n , 1 ) a sequence of discrete and faithful representations, then the geometric limit of ρ i ( Γ ) is a discrete subgroup of SO ( n , 1 ) . We generalize this result by...

On groups of similitudes in associative rings

Evgenii L. Bashkirov (2008)

Commentationes Mathematicae Universitatis Carolinae

Let R be an associative ring with 1 and R × the multiplicative group of invertible elements of R . In the paper, subgroups of R × which may be regarded as analogues of the similitude group of a non-degenerate sesquilinear reflexive form and of the isometry group of such a form are defined in an abstract way. The main result states that a unipotent abstractly defined similitude must belong to the corresponding abstractly defined isometry group.

On L-Groups.

David B. Wales, Hans J. Zassenhaus (1972)

Mathematische Annalen

On Macbeath-Singerman symmetries of Belyi surfaces with PSL(2,p) as a group of automorphisms

Ewa Tyszkowska (2003)

Open Mathematics

The famous theorem of Belyi states that the compact Riemann surface X can be defined over the number field if and only if X can be uniformized by a finite index subgroup Γ of a Fuchsian triangle group Λ. As a result such surfaces are now called Belyi surfaces. The groups PSL(2,q),q=p n are known to act as the groups of automorphisms on such surfaces. Certain aspects of such actions have been extensively studied in the literature. In this paper, we deal with symmetries. Singerman showed, using acertain...

On pq-hyperelliptic Riemann surfaces

Ewa Tyszkowska (2005)

Colloquium Mathematicae

A compact Riemann surface X of genus g > 1 is said to be p-hyperelliptic if X admits a conformal involution ϱ, called a p-hyperelliptic involution, for which X/ϱ is an orbifold of genus p. If in addition X admits a q-hypereliptic involution then we say that X is pq-hyperelliptic. We give a necessary and sufficient condition on p,q and g for existence of a pq-hyperelliptic Riemann surface of genus g. Moreover we give some conditions under which p- and q-hyperelliptic involutions of a pq-hyperelliptic...

On soluble groups of module automorphisms of finite rank

Bertram A. F. Wehrfritz (2017)

Czechoslovak Mathematical Journal

Let R be a commutative ring, M an R -module and G a group of R -automorphisms of M , usually with some sort of rank restriction on G . We study the transfer of hypotheses between M / C M ( G ) and [ M , G ] such as Noetherian or having finite composition length. In this we extend recent work of Dixon, Kurdachenko and Otal and of Kurdachenko, Subbotin and Chupordia. For example, suppose [ M , G ] is R -Noetherian. If G has finite rank, then M / C M ( G ) also is R -Noetherian. Further, if [ M , G ] is R -Noetherian and if only certain abelian sections...

On some infinite dimensional linear groups

Leonid Kurdachenko, Alexey Sadovnichenko, Igor Subbotin (2009)

Open Mathematics

Let F be a field, A be a vector space over F, and GL(F,A) the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dimF(B/CoreG(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF.

Currently displaying 221 – 240 of 505