On Finite Solvable Groups G with m(G)-d(G)=1  

作　　者：Hailin LIU Liping ZHONG Shoushuang CHEN Yulong MA 

机构地区：[1]School of Science,Jiangxi University of Science and Technology,Jiangxi 341000,P.R.China [2]School of Mathematics,Northwest University,Shaanxi 710127,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2025年第1期33-38,共6页数学研究及应用(英文版)

基　　金：Supported by China Scholarship Council(Grant No.202208360148);the National Natural Science Foundation of China(Grant Nos.12126415,12261042,12301026);the Natural Science Foundation of Jiangxi Province(Grant No.20232BAB211006).

摘　　要：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)≥m(G/N)+m(N)for any non-trivial normal subgroup N of G.

关 键 词：finite solvable group minimal generating set normal subgroup cyclic group 

分 类 号：O152.1[理学—数学]