| On Finite Solvable Groups $G$ with $m(G)-d(G)=1$ |
| Received:July 14, 2024 Revised:October 11, 2024 |
| Key Words:
finite solvable group minimal generating set normal subgroup cyclic group
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| Fund Project:Supported by China Scholarship Council (Grant No.202208360148), the National Natural Science Foundation of China (Grant Nos.12126415; 12261042; 12301026) and the Natural Science Foundation of Jiangxi Province (Grant No.20232BAB211006). |
| Author Name | Affiliation | | Hailin LIU | School of Science, Jiangxi University of Science and Technology, Jiangxi 341000, P. R. China | | Liping ZHONG | School of Science, Jiangxi University of Science and Technology, Jiangxi 341000, P. R. China | | Shoushuang CHEN | School of Science, Jiangxi University of Science and Technology, Jiangxi 341000, P. R. China | | Yulong MA | School of Mathematics, Northwest University, Shaanxi 710127, P. R. China |
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| Abstract: |
| Let $G$ be a finite group. A generating set $X$ of $G$ is said to be minimal if no proper subset of $X$ generates $G$. Let $d(G)$ and $m(G)$ denote the smallest size and the largest size of a minimal generating set of $G$, respectively. In this paper we present a characterization for finite solvable groups $G$ such that $m(G)-d(G)=1$ and $m(G)\geq m(G/N)+m(N)$ for any non-trivial normal subgroup $N$ of $G$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2025.01.004 |
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