Crystalline concept is the main concept used as the reference by students in algebraic verification. This concept divided the way of solving algebraic verification into two types: symbolic and embodied compression. This research aimed to explore the students' mathematical thinking process in solving algebraic verification based on the Crystalline concept types. The subjects of research were 15 students who took abstract algebra course. Those subjects were asked to solve algebraic verification and were divided based on their types. To get a deeper data, one student was randomly chosen from each type to be interviewed. The verification and interview data were analyzed by using the steps of mathematical thinking process. Those steps are abstracting, representation, and verification. Abstracting is the step to find the ideas: definition of group and abelian group. Representation is the way to communicate the suitable ideas with the conditions. The last step is verification in which students performed the process based on the results of two previous steps. The symbolic student tends to solve the verification symbolically while the embodied one solved the verification arithmetically. Based on the findings, it is essential to design a learning that can accustom students to solve algebraic verification symbolically as the verification should be done deductively.