26 citations · 63 across the 9 of their papers we have counts for
8 papers · 1 filter
Symmetric Groups and Expander Graphs
Martin Kassabov
We construct explicit generating sets S_n and \tilde S_n of the for the alternating and the symmetric groups, which turn the Cayley graphs C(Alt(n), S_n) and C(Sym(n), \tilde S_n)…
Symmetric Groups and Expanders
Martin Kassabov
We construct an explicit generating sets and of the alternating and the symmetric groups, which make the Cayley graphs and $C(Sym(n), \tilde F_n…
Universal lattices and unbounded rank expanders
Martin Kassabov
We study the representations of non-commutative universal lattices and use them to compute lower bounds for the \TauC for the commutative universal lattices $G_{d,k}= \SL_d(\Z[x_1,…
Diameters of Cayley graphs of SL_n(Z/kZ)
M. Kassabov, T. R. Riley
We show that for integers k > 1 and n > 2, the diameter of the Cayley graph of SL_n(Z/kZ) associated to a standard two-element generating set, is at most a constant times n^2 ln k.…
Weak Identities in finitely generated groups
Martin Kassabov
In this article we introduce the notion of weak identities in a group and study their properties. We show that weak identities have some similar properties to ordinary ones. We use…
An Automorphism of A Free Metabelian Group Without Fixed Points
Martin Kassabov
We construct an example of an IA-automorphism of the free metabelian group of rank without nontrivial fixed points. That gives a negative answer to the question raised by…