Binzhou Xia

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20242026

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3 papers · 1 filter

math.GR2026

Almost all finite groups are $2$ -groups of class two

Ning Su, Binzhou Xia

We prove that almost all finite groups are $2$ -groups of nilpotency class two, when groups of order at most $x$ are counted up to isomorphism and $x \to \infty$ . More precisely, unif…

math.GR2026

Automorphism groups of Cayley graphs on almost simple groups with normal connection sets

Mengyu Cao, Benjian Lv, Binzhou Xia

We determine the full automorphism group of every connected Cayley graph on an almost simple group with a normal connection set. We also characterize exactly when the full automorp…

math.GR2026

Solvable Supplements to Normalizers of Cyclic 2-Subgroups

Shou Hong Qiao, Binzhou Xia

Amberg and Kazarin proved that a finite group is solvable if the normalizer of every cyclic subgroup of prime power order has a solvable supplement. We substantially relax this hyp…

Almost all finite groups are 2-groups of class two

Automorphism groups of Cayley graphs on almost simple groups with normal connection sets

Solvable Supplements to Normalizers of Cyclic 2-Subgroups

Almost all finite groups are $2$ -groups of class two