37 citations · 51 across the 16 of their papers we have counts for
18 papers
Polycyclic groups and profinite isomorphism
Dan Segal
The Profinite Isomorphism Problem for a class of groups \mathcal{C} asks for an algorithm that decides for any two groups in \mathcal{C} whether they have isomorphic profinite comp…
On the finite axiomatizability of some metabelian profinite groups
Dan Segal
Finitely generated (non-abelian) free metabelian pro-p groups, and wreath products of f.g. free abelian pro-p groups, are all finitely axiomatizable in the class of all profinite g…
Commensurability and bi-interpretability of groups
Dan Segal
Commensurable groups are bi-interpretable, under suitable definability conditions.
A profinite analogue of Lasserre's theorem
Dan Segal
A soluble pro-p group of finite rank is finitely axiomatizable in the class of all profinite groups if and only if for each open subgroup H, the image of Z(H) in the abelianization…
Constructing uncountably many groups with the same profinite completion
Nikolay Nikolov, Dan Segal
We present two uncountable families of finitely generated residually finite groups all having the same profinite completion. One consists of soluble groups, the other of branch gro…
On groups of finite upper rank
Dan Segal
The `upper rank' of a group is the supremum of the (Prüfer) ranks of its finite quotients, and for a prime , the `upper -rank' is the supremum of the sectional -ranks of t…