R. Shen

activity

20152026

most citedFinite simple groups with some abelian Sylow subgroups

6 citations · 6 across the 5 of their papers we have counts for

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5 papers · 1 filter

math.GR2026

On Zappa's question in the case of alternating groups

Ru Zhang, Rulin Shen

In 1962, Guido Zappa asked whether a non-trivial coset of a Sylow $p$ -subgroup of a finite group could contain only elements whose orders are powers of $p$ . Marston Conder gives a…

math.GR2023

On Thompson Problem

Rulin Shen, Wujie Shi, Feng Tang

In 1987, the second author of this paper reported his conjecture, all finite simple groups $S$ can be characterized uniformly using the order of $S$ and the set of element orders i…

math.GR2022

Finite groups in which every maximal subgroup is nilpotent or normal or has $p^{'}$ -order

Jiangtao Shi, Na Li, Rulin Shen

Let $G$ be a finite group and $p$ a fixed prime divisor of $∣ G ∣$ . Combining the nilpotence, the normality and the order of groups together, we prove that if every maximal subgroup…

math.GR2020

The second minimum/maximum value of the number of cyclic subgroups of finite $p$ -groups

Mihai-Silviu Lazorec, Rulin Shen, Marius Tărnăuceanu

Let $C (G)$ be the poset of cyclic subgroups of a finite group $G$ and let $P$ be the class of $p$ -groups of order $p^{n}$ ( $n \geq 3$ ). Consider the function $α:\mathcal{P}\…

math.GR2015★ 6 cited

Finite simple groups with some abelian Sylow subgroups

Rulin Shen, Yuanyang Zhou

In this paper, we classify the finite simple groups with an abelian Sylow subgroup.

On Zappa's question in the case of alternating groups

On Thompson Problem

Finite groups in which every maximal subgroup is nilpotent or normal or has p′-order

The second minimum/maximum value of the number of cyclic subgroups of finite p-groups

Finite simple groups with some abelian Sylow subgroups

Finite groups in which every maximal subgroup is nilpotent or normal or has $p^{'}$ -order

The second minimum/maximum value of the number of cyclic subgroups of finite $p$ -groups