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The purpose of this study was to describe students' understanding of the group concept. The focus of the research is students' understanding of the group concept which is very important because the group concept is a basic concept in group theory courses. This research is a qualitative research with descriptive method. Subjects in this study were fourth semester students in class E in Mathematics Education Department at Education Science Faculty at University of Singaperbangsa. The instrument used in this study is a test. The results showed, The Student's understanding with high mathematical abilities can prove the group to be closed, associative, have an identity element and have an inverse according to its definition. For students with medium mathematical abilities They are not proof of the existence of inverse in a set which is a group or not a group. And for student with low mathematical abilities understanding is only limited to understanding the charesteristic of closeness for the requirements of a group.

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