3 papers
math.GR2005
Finite Groups of Uniform Logarithmic Diameter
Miklos Abert, Laszlo Babai
We give an example of an infinite family of finite groups such that each can be generated by 2 elements and the diameter of every Cayley graph of is $O(\log (| G_…
math.GR2005
On the probability of satisfying a word in a group
Miklos Abert
We show that for any finite group and for any there exists a word such that a -tuple in satisfies if and only if it generates a solvable subgroup. I…
math.GR2003
Group laws and free subgroups in topological groups
Miklos Abert
We prove that a permutation group in which different finite sets have different stabilizers cannot satisfy any group law. For locally compact topological groups with this property…