Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/1320 2022 2022 Sarkismaretta1990@gmail.com Maretta Sarkis In this work, we study the extension problem of a group with type C(n)=∑_(i∈I) C_P^∞  by using a cyclic group of order p. Also, we prove the following two results: 1-) The group C(n)  has only one extension which is compatible with R_3. 2-) The group C(n) has two extensions which are compatible with R_2. 2022 2022 11 12 10.54216/GJMSA.010202 https://www.americaspg.com/articleinfo/33/show/1320