Pictures on the second homotopy module of the group from Kronecker product on the representation quaternion group

Abstract

Abstract This paper discusses pictures on the second homotopy module of the group from the Kronecker product on the representation quaternion group. It needs three notions to construct the second homotopy module, which is the presentation of the group, word, and spherical picture. In this paper, it has used the presence of a group that is obtained from the group Kronecker product on the representation of the quaternion group. This presentation has four generators and five relations. Based on this presentation, we got word, and then a picture can be drawn. It uses van Kampen Lemma to construct the picture and operation on picture to obtain a spherical picture. It has presented pictures with one and all of the generators in the presentation of the group. It has used relations in the presentation of a group to make the picture become a spherical picture. We conclude that the spherical picture, which becomes generators built all pictures.