Bernardo Giuseppe Di Siena

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math.GR2026

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 $G$ which is not an…

math.GR2026

A torsion-free group of nilpotency class six with all subgroups subnormal of defect at most $5$

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 $n$ must be nilpotent of class at most $n$ . The answer is known to be positive for…

math.GR2026

An antichain condition for infinite groups

Mattia Brescia, Bernardo Di Siena, Alessio Russo

Let $χ$ be a subgroup-theoretical property. We introduce an \emph{antichain condition} $ac_{χ}$ which forbids the existence of infinite antichains of mutually permutab…

The group class SJ is not countably recognizable

A torsion-free group of nilpotency class six with all subgroups subnormal of defect at most 5

An antichain condition for infinite groups

A torsion-free group of nilpotency class six with all subgroups subnormal of defect at most $5$