Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/1321 2022 2022 Imam Kadhum College, Iraq A. Alrida .. University Of Nizwa, Nizwa, Oman Oliver V. .. Abu Dhabi University, Abu Dhabi, UAE Maretta .. Cairo University, Egypt Rozina Ali This paper is dedicated to study some properties of finite groups, where we present the following results: 1) If all centralizers of a group G are cyclic, then G is not simple. 2) If the center of the subgroup A is not trivial and B is cyclic, then G=AB is not simple. On the other hand, we define the m-solvable groups, and we examine some of their elementary properties. 2022 2022 13 16 10.54216/GJMSA.010203 https://www.americaspg.com/articleinfo/33/show/1321