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We prove that Cannon–Thurston maps are well–defined (that is, subgroup inclusion induces a map of the boundaries) for heavily distorted free subgroups inside the family of hyperbolic groups known as h...
THE SUBGROUP ALGORITHM FOR GENERATING UNIFORM RANDOM VARIABLES.
We show that if G is a nontrivial, finite group of odd order, whose commutator subgroup [G,G] is cyclic of order p^m q^n, where p and q are prime, then every connected Cayley graph on G has a hamilton...
Abstract: In 2003 COHN and UMANS introduced a group-theoretic approach to fast matrix multiplication. This involves finding large subsets of a group $G$ satisfying the Triple Product Property (TPP) as...
Abstract: In the context of group-theoretic fast matrix multiplication the TPP capacity is used to bound the exponent $\omega$ of matrix multiplication. We prove a new and sharper upper bound for the ...
Abstract: We present a method to obtain congruences modulo powers of 2 for sequences given by recurrences of finite depth with polynomial coefficients. We apply this method to Catalan numbers, Fu\ss-C...
We give a list of finite groups containing all finite groups G such that the group of units ZG∗ of the integral group ring ZG is subgroup separable. There are only two types of these groups G fo...
A group G is called subgroup conjugacy separable (abbreviated as SCS), if any two finitely generated and non-conjugate subgroups of G remain non-conjugate in some finite quotient of G. We prove that t...
In 2007, B. Poonen (unpublished) studied the p{adic closure of a subgroup of rational points on a commutative algebraic group. More recently, J. Bellache asked the same question for the special case...
Let R be a commutative ring with 1, and let G be an isotropic reductive algebraic group over R. In [5] Victor Petrov and the second author introduced a notion of an elementary subgroup E(R) of the gro...
We study the complex of partial bases of a free group, which is an analogue for Aut(Fn) of the curve complex for the mapping class group. We prove that it is connected and simply connected, and we a...
We show that if G is a finite group then no chain of modular elements in its subgroup lattice L(G) is longer than a chief series. Also, we show that if G is a nonsolvable finite group then every maxi...
In a recent contribution, Tˇarnˇauceanu has introduced the subgroup commutativity degree of a finite group,adapting to the context of the lattice theory some ideas and some techniques, which were know...
We study the effects of subgroup distortion in the wreath products A wr Z, where A is finitely generated abelian. We show that every finitely generated subgroup of A wr Z has distortion function bound...
We prove that each infinite 2-group G with a unique 2-element subgroup is isomorphic either to the quasicyclic 2-group C21 or to the infinite group of generalized quaternions Q21. The latter group is...

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