Author

Bin-Zhou Xia

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Preprint Oct 2026

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

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, uniformly for $2^m\leq x<2^{m+1}$, all but an $O(2^{-cm^2})$ proportion have order $2^m$ and class two, for some absolute constant $c>0$. For ea...

Ning Su, Bin-Zhou Xia · 0 citations

Preprint Sep 2026

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

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 automorphism group is generated by right translations, group automorphisms preserving the connection set, and inversion. Our results substantially g...

Meng-Yue Cao, Ben-Jian Lv, Bin-Zhou Xia · 0 citations