Xingzhong Xu

activity

20172021

B

-groups

2 citations · 4 across the 9 of their papers we have counts for

collaborators

9 papers

math.GR2021

A weak form of a conjecture on vanishing of group cohomology for blocks

Heguo Liu, Xingzhong Xu, Jiping Zhang

In this paper, we get an elementary and important lemma(See Lemma 3.2) which is about pushout and pullback of modules. And we prove a weak form of a long open conjecture on vanishi…

math.GR2020

Some results on a question of M. Newman on isomorphic subgroups of solvable groups

Heguo Liu, Xingzhong Xu, Jiping Zhang

In this paper, we focus on a question of M. Newman on isomorphic subgroups of solvable groups. We get a reduction theorem of this question: for each prime q, assume that this quest…

math.GR2019

A bound for Hall's criterion for nilpotence in semi-abelian categories

Heguo Liu, Xingzhong Xu, Jiping Zhang

In this paper, we focus on Hall's criterion for nilpotence in semi-abelian categories, and we improve the bound of Gray's main theorem of [3,Theorem 3.4] (see Main Theorem). And th…

math.GR2018

A topological interpretation about $m_{G, N}$ for finite group $G$ with normal subgroup $N$

Heguo Liu, Xingzhong Xu, Jiping Zhang

Let $G$ be a finite group and $N ⊴ G$ . In this note, we construct a class poset of $G$ for some cyclic subgroup $C$ of $G$ . And we find a relation between $m_{G, N}$ and the Eul…

math.GR2017

A note on Oliver's p-group conjecture

Xingzhong Xu

Let $S$ be a $p$ -group for an odd prime $p$ , Oliver proposed the conjecture that the Thompson subgroup $J (S)$ is always contained in the Oliver subgroup $X (S)$ . That mea…

math.GR2017

Elementary abelian subgroups in some special p-groups

Xingzhong Xu

Let $P$ be a finite $p$ -group and $p$ be an odd prime. Let $A_{p} (P)_{\geq 2}$ be a poset consisting of elementary abelian subgroups of rank at least 2. If the derived subgr…

math.GR2017★ 1 cited

A relation between $m_{G, N}$ and the Euler characteristic of the nerve space of some class poset of $G$

Heguo Liu, Xingzhong Xu, Jiping Zhang

Let $G$ be a finite group and $N ⊴ G$ with $∣ G : N ∣ = p$ for some prime $p$ . In this note, to compute $m_{G, N}$ directly, we construct a class poset $T_{C} (G)$ of $G$ f…

math.GR2017★ 2 cited

Bouc's conjecture on $B$ -groups

Xingzhong Xu, Jiping Zhang

Bouc proposed the following conjecture: a finite group $G$ is nilpotent if and only if its largest quotient $B$ -group $β (G)$ is nilpotent. And he has prove that this conjecture hol…

math.GR2017★ 1 cited

Fusion systems of blocks with nontrivial strongly closed subgroups

Heguo Liu, Xingzhong Xu, Jiping Zhang

In this paper, we find some exotic fusion systems which have non-trivial strongly closed subgroups, and we prove these fusion systems are also not realizable by p-blocks of finite…

A weak form of a conjecture on vanishing of group cohomology for blocks

Some results on a question of M. Newman on isomorphic subgroups of solvable groups

A bound for Hall's criterion for nilpotence in semi-abelian categories

A topological interpretation about mG,N​ for finite group G with normal subgroup N

A note on Oliver's p-group conjecture

Elementary abelian subgroups in some special p-groups

A relation between mG,N​ and the Euler characteristic of the nerve space of some class poset of G

Bouc's conjecture on B-groups

Fusion systems of blocks with nontrivial strongly closed subgroups

A topological interpretation about $m_{G, N}$ for finite group $G$ with normal subgroup $N$

A relation between $m_{G, N}$ and the Euler characteristic of the nerve space of some class poset of $G$

Bouc's conjecture on $B$ -groups