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math.GR2026
Groups satisfying Gaschütz's complement theorem
Stefanos Aivazidis, Benjamin Sambale
A classical theorem of Gaschütz states that an abelian normal subgroup N of a finite group G has a complement in G whenever it has a complement in some subgroup H with $N \leq H \l…
math.GR2026
Subgroup bounds for abelian -groups with applications
Stefanos Aivazidis
We prove an upper bound for the number of subgroups of an abelian -group, with constants that are sharp on homocyclic blocks. If has type , the main exponent is $η(λ)=\…