@article { author = {Zhang, C.}, title = {On non-normal non-abelian subgroups of finite groups}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {43}, number = {3}, pages = {659-663}, year = {2017}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {‎In this paper we prove that a finite group $G$ having at most three‎ ‎conjugacy classes of non-normal non-abelian proper subgroups is‎ ‎always solvable except for $G\cong{\rm{A_5}}$‎, ‎which extends Theorem 3.3‎ ‎in [Some sufficient conditions on the number of‎ ‎non-abelian subgroups of a finite group to be solvable‎, ‎Acta Math‎. ‎Sinica (English Series) 27 (2011) 891--896.]‎. ‎Moreover‎, ‎we show that a‎ ‎finite group $G$ with at most three same order classes of non-normal‎ ‎non-abelian proper subgroups is always solvable except for $G\cong‎{A_5}$‎.}, keywords = {Non-abelian subgroup‎,‎non-normal‎,‎conjugacy class‎,‎same order class‎}, url = {http://bims.iranjournals.ir/article_955.html}, eprint = {http://bims.iranjournals.ir/article_955_337a7def7f393b8d74b7c0e4c79047e1.pdf} }