COPRIME DEGREE OF SOME GROUPS AND ITS RELATION TO COPRIME GRAPHS
Coprime degree of a group can be seen as a generalization of commutativity degree of a group. Coprime degree of a group is defined to be the probability that two random elements in the group have coprime orders. Meanwhile, the coprime graph of a finite group is a graph where the set of vertices i...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/73410 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Coprime degree of a group can be seen as a generalization of commutativity degree
of a group. Coprime degree of a group is defined to be the probability that two
random elements in the group have coprime orders. Meanwhile, the coprime graph
of a finite group is a graph where the set of vertices is a elements of a group, and
two distinct vertices are adjacent if their order is coprime. In this paper, we derive
explicit description of coprime degree for several finite groups with respect to
the prime decompositions of their group orders, including cyclic groups, dihedral
groups, and generalized quaternion groups. Furthermore, we establish the relation
between coprime degree of a group and its coprime graph |
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