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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 is a non-elementary finitely generated group and a sequence of discrete and faithful representations, then the geometric limit of is a discrete subgroup of . We generalize this result by...
Let be an associative ring with 1 and the multiplicative group of invertible elements of . In the paper, subgroups of 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.
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...
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...
Let be a commutative ring, an -module and a group of -automorphisms of , usually with some sort of rank restriction on . We study the transfer of hypotheses between and 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 is -Noetherian. If has finite rank, then also is -Noetherian. Further, if is -Noetherian and if only certain abelian sections...
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.
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