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math.GR2025
On finite groups with soluble centralisers
Valentina Grazian, Carmine Monetta, Gareth Tracey
We classify finite groups in which the centralisers of certain non-central elements are soluble. This includes a full structural description of groups whose non-central element cen…
math.GR2023
Group nilpotency from a graph point of view
Valentina Grazian, Andrea Lucchini, Carmine Monetta
Let denote a graph associated with a group . A compelling question about finite groups asks whether or not a finite group must be nilpotent provided is isomorphi…
math.GR2023
A conjecture related to the nilpotency of groups with isomorphic non-commuting graphs
Valentina Grazian, Carmine Monetta
In this work we discuss whether the non-commuting graph of a finite group can determine its nilpotency. More precisely, Abdollahi, Akbari and Maimani conjectured that if and $H…