4 papers · 1 filter
Almost all finite groups are -groups of class two
Ning Su, Binzhou Xia
We prove that almost all finite groups are -groups of nilpotency class two, when groups of order at most are counted up to isomorphism and . More precisely, unif…
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…
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…
On biprimitive semisymmetric graphs
Yunsong Gan, Weijun Liu, Binzhou Xia
A regular bipartite graph is called semisymmetric if its full automorphism group acts transitively on the edge set but not on the vertex set. For a subgroup $…