FINITE_GROUPS

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Character codegrees in finite groups
《Frontiers of Mathematics in China》2023年第1期15-32,共18页Guohua QIAN 
support provided by the National Natural Science Foundation of China(Grant No.12171058).
For an irreducible character x of a finite group G,we define its codegree as cod(x)=|G:ker x|/x(1) .In this paper,we introduce some known results x(1)and unsolved problems about character codegrees in finite groups.
关键词：Finite group CHARACTER character codegree 
Semipermutable subgroups and s-semipermutable subgroups in finite groups
《Frontiers of Mathematics in China》2022年第1期23-46,共24页Yangming LI 
supported in part by the project of NSF of China(12071092);the Science and Technology Program of Guangzhou Municipality,China(201804010088).
Suppose that H is a subgroup of a finite group G.We call H is semipermutable in G if HK=KH iov any subgroup K of G such that(|H|,|K|)=1;H is s-semipermutable in G if HG_(p)=G_(p)H,for any Sylow p-subgroup G_(p)of G su...
关键词：Semipermutable subgroup s-semipermutable subgroup maximal subgroup minimal subgroup the generalized Fitting-subgroup formation 
On p-CAP-subgroups of finite groups
《Frontiers of Mathematics in China》2020年第5期915-921,共7页Zhichao GAO Shonhong QIAO Huaguo SHI Long MIAO 
supported by the National Natural ScienceFoundation of China(Grant Nos.11871062,12071093);the NSFC-RFBR(Grant No.12011530061);the Natural Science Foundation of Jiangsu Province(Grant No.BK20181451).
Suppose that G is a finite group and H is a subgroup of G.H is said to be a p-CAP-subgroup of G if H either covers or avoids each pd-chief factor of G.We give some characterizations for a group G to be p-solvable unde...
关键词：Maximal subgroups 2-maximal subgroups p-CAP-subgroups 
On c#-normal subgroups in finite groups被引量：2
《Frontiers of Mathematics in China》2018年第5期1169-1178,共10页Huaquan WEI Qiao DAI Hualian ZHANG Yubo LV Liying YANG 
A subgroup H of a finite group G is called a c#-normal subgroup of G if there exists a normal subgroup K of G such that G = HK and H n K is a CAP-subgroup of G. In this paper, we investigate the influence of fewer c#-...
关键词：Finite group c#-normal p-supersolvable P-NILPOTENT SUPERSOLVABLE 
Solvability of finite groups
《Frontiers of Mathematics in China》2017年第6期1501-1514,共14页Jia ZHANG Baijun GAO Long MIAO 
This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11271016, 11501235）, the Qing Lan Project of Jiangsu Province, the High-level Personnel of Support Program of Yangzhou University, the Natural Science Foundation of Xinjiang Uygur Autonomous Region （Grant No. 2016D01C387）, and the Key Natural Science Foundation of Anhui Education Commission （KJ2017A569）.
H is called an Mp-embedded subgroup of G, if there exists a pnilpotent subgroup B of G such that Hp E Sylp（B） and B is Mp-supplemented in G. In this paper, by considering prime divisor 3, 5, or 7, we use Mp-embedded...
关键词：Composition factor Mp-embedded subgroup primary subgroup SOLVABLE 
Finite groups with permutable Hall subgroups被引量：1
《Frontiers of Mathematics in China》2017年第5期1265-1275,共11页Xia YIN Nanying YANG 
Throughout this paper, all groups are finite and G always denotes a finite group. We use π（G） to denote the set of all primes dividing ｜G｜. A subgroup A of G is said to permute with a subgroup B if AB = BA. In th...
关键词：Finite group Hall subgroup complete Hall or-set permutablesubgroup supersoluble group 
S-semiembedded subgroups of finite groups被引量：2
《Frontiers of Mathematics in China》2015年第6期1401-1413,共13页Yuemei MAO Abid MAHBOOB Wenbin GUO 
Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11371335） and the Specialized Research Fund for the Doctoral Program of Higher Education of China （Grant #20113402110036）.
A subgroup H of a finite group G is said to be s-semipermutable in G if it is permutable with every Sylow p-subgroup of G with （p, ｜H｜） = 1. We say that a subgroup H of a finite group G is S-semiembedded in G if t...
关键词：s-Permutable subgroup s-semipermutable subgroup supersoluble group S-semiembedded subgroup p-nilpotent group 
On weakly s-permutably embedded subgroups of finite groups （II）
《Frontiers of Mathematics in China》2013年第4期855-867,共13页Yujian HUANG Yangming LI Shouhong QIAO 
This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11271085, 11201082）, the Natural Science Foundation of Guangdong Province （S2011010004447）, and the Special Project for the Subject Build of High Education of Guangdong Province （2012KJCX0081）.
Suppose that G is a finite group and H is a subgroup of G. H is said to be s-permutably embedded in G if for each prime p dividing ｜H｜, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-permutable subgrou...
关键词：s-Permutable subgroup s-permutably embedded subgroup weakly s-permutably embedded subgroup p-nilpotent group 
c^＊-Quasinormally embedded subgroups of finite groups被引量：1
《Frontiers of Mathematics in China》2012年第4期703-716,共14页Changwen LI Jianhong HUANG Bin HU 
This work was supported in part by the National Natural Science Foundation of China （Grant No. 11071229） and the Natural Science Foundation the Jiangsu Higher Education Institutions （Grant No. J0KJD110004）.
Suppose that G is a finite group and H is a subgroup of G. H is said to be s-quasinormally embedded in G if for each prime p dividing │H│, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-quasinormal sub...
关键词：c^＊-Quasinormally embedded subgroup P-NILPOTENT SUPERSOLVABLE Sylow subgroup 
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