Related papers: A Borel maximal cofinitary group

We establish basic results on subrings of finite commutative rings and closely related rings. Among other applications we calculate the number of maximal subrings of a finite commutative local ring.

We give an example of a finitely presented simple group containing a finitely generated subgroup which is not finitely presented.

We determine the abelian invariants of the maximal tori in the finite spin groups of type $D_l$

We present a proof of a result, previously announced by the second author, that there is a closed (even $\Pi^0_1$) set generating an $F_\sigma$ (even $\Sigma^0_2$) maximal cofinitary group (short, mcg) which is isomorphic to a free group.…

We classify the maximal algebraic subgroups of Bir(CxPP^1), when C is a smooth projective curve of positive genus.

We prove several results on the structure of solvable quotients of fundamental groups of compact Kahler manifolds (Kahler groups).

We review the results having the property of maximal transcendentality.

We survey some results on toric topology.

Higher order cohomology of arithmetic groups is expressed in terms of (g,K)-cohomology. Generalizing results of Borel, it is shown that the latter can be computed using functions of (uniform) moderate growth. A higher order versions of…

In this paper, the complete algebraic structure of finite semisimple group algebra of a normally monomial group is described. The main result is illustrated by computing the explicit Wedderburn decomposition of finite semisimple group…

In this paper we obtain an explicit formula for the higher Schur-multiplicator of an arbitrary finite abelian group with respect to the variety of nilpotent groups of class at most $c\geq 1$ .

We give a description of finitely generated prosoluble subgroups of the profinite completion of $3$-manifold groups and virtually compact special groups.

We introduce the notion of a tight cofinitary group, which captures forcing indestructibility of maximal cofinitary groups for a long list of partial orders, including Cohen, Sacks, Miller, Miller partition forcing and Shelah's poset for…

We construct a family of finitely generated infinite periodic groups. The basic example is a 2-group, called the tetrahedron group. We generalize the construction by suggesting a family of infinite finitely generated dice groups. We provide…

We present an elliptic version of Selberg's integral formula.

Recent results on finite open group transformations are reviewed.

To follow up on the results of [1], we propose a computationally efficient explicit cyclic decomposition of the maximal tori in the groups $SL_n(q)$ and $SU_n(q)$ and their projective images. We also derive some corollaries to simplify…

We study the structure of combinatorial Burnside groups, which receive equivariant birational invariants of actions of finite groups on algebraic varieties.

The complete algebraic structure of semisimple finite group algebra of a generalized strongly monomial group is provided. This work extends the work of Broche and del R{\'{\i}}o on strongly monomial groups. The theory is complimented by an…

In this paper we obtain significant bounds for the number of maximal subgroups of a given index of a finite group. These results allow us to give new bounds for the number of random generators needed to generate a finite $d$-generated group…