A Note on Special Local 2-Nilpotent Groups and the Solvability of Finite Groups

作     者：Jiangtao Shi Klavdija Kutnar Cui Zhang 

作者机构：School of Mathematics and Information SciencesYantai University YantaiShandong 264005China University of PrimorskaFAMNITGlagoljaska 86000 KoperSlovenia University of PrimorskaIAMMuzejski trg 26000 KoperSlovenia School of Mathematics and Information ScienceYantai University YantaiShandong 2640058China 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2018年第25卷第4期

页      面：541-546页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Shandong Provincial Natural Science Foundation,China(ZR2017MA022) NSFC(11561021 and 11761079) Slovenian Research Agency(research program P1-0285 research projects N1-0038,N1-0062,J1-6720,J1-6743,J1-7051,J1-9110) in part by NSFC(11561021) NSFC(11201403 and 11561021) 

主　　题：quaternion group 2-nilpotent group solvable group 

摘      要：A finite group G is called a special local 2-nilpotent group if G is not 2-nilpotent,the Sylow 2-subgroup P of G has a section isomorphic to the quaternion group of order 8,Ω(P∩G )≤Z(P)and NG(P)is *** this paper,it is shown that SL2(q),q3,is a special local 2-nilpotent group if and only if q^2≡1(mod 16),and that GL2(q),q3,is a special local 2-nilpotent group if and only if q is ***,the solvability of finite groups is also investigated by giving two generalizations of a result from[A note on p-nilpotence and solvability of finite groups,*** 321(2009)1555-1560].