5 papers
Abelian state-closed subgroups of automorphisms of m-ary trees
Andrew M. Brunner, Said N. Sidki
The group A_{m} of automophisms of a one-rooted m-ary tree admits a diagonal monomorphism which we denote by x. Let A be an abelian state-closed (or self-similar) subgroup of A_{m}…
Functionally recursive rings of matrices-Two examples
Said N. Sidki
We define the notions of finite-state and functionally recursive matrices and their growth. We also introduce two rings generated by functionally recursive matrices. The first is i…
On Commutativity and Finiteness in Groups
Ricardo N. Oliveira, Said N. Sidki
The second author introduced notions of weak permutability and commutativity between groups and proved the finiteness of a group generated by two weakly permutable finite groups. T…
Virtual Endomorphisms of Nilpotent Groups
Adilson Berlatto, Said Sidki
A virtual endomorphism of a group G is a homomorphism f from H into G where H is a subgroup of G of finite index m. The triple (G,H,f) produces a state-closed (or, self-similar) re…
On pairs of matrices generating matrix rings and their presentations
B. V. Petrenko, S. N. Sidki
Let the ring of -by- matrices with integral entries, and . This paper studies the set of pairs gen…