6 papers · 2 filters
The group class SJ is not countably recognizable
M. Brescia, B. G. Di Siena, E. Ingrosso +1
A group is an {\it $\SJ$-group} if it admits a general abelian series all of whose terms are subnormal of finite defect in the whole group. We construct a group which is not an…
On the independence of permutation characters
M. Brescia, E. Ingrosso, M. Trombetti
Let be a finite group. For every subgroup , let be the permutation character of the action of on the left cosets of . We prove that the characters ,…
A torsion-free group of nilpotency class six with all subgroups subnormal of defect at most
Mattia Brescia, Bernardo Giuseppe Di Siena, Marco Trombetti
Casolo asked whether a torsion-free group in which every subgroup is subnormal of defect at most must be nilpotent of class at most . The answer is known to be positive for…
Hopficity of profinite completions of abelian groups
M. Brescia, E. Ingrosso, M. Trombetti
We determine exactly when the profinite completion of an arbitrary abelian group is topologically Hopfian. For an abelian group , we prove that \[ \widehat A \text{ is topologic…
A Torsion-free Supersoluble Group with Trivial Outer Automorphism Group
Mattia Brescia, Ernesto Ingrosso, Marco Trombetti
We give a negative solution to Problem~13.23 of the Kourovka Notebook. We construct a torsion-free group of Hirsch length admitting a finite series \[ 1=G_0\triangleleft G…
An antichain condition for infinite groups
Mattia Brescia, Bernardo Di Siena, Alessio Russo
Let be a subgroup-theoretical property. We introduce an \emph{antichain condition} which forbids the existence of infinite antichains of mutually permutab…