GRUP NON-ABELIAN YANG ABELIAN SECARA GRAFIS
Abstract: A group 𝐺 is graphically abelian if
the map that pairs each element of the group 𝐺 to its inverse is an
automorphism of every Cayley graph of 𝐺. So, all abelian groups
are graphically abelian. The purpose of this research is to show the
characterization of non-abelian group which is graphically abelian group. By
reviewing the properties of groups and graphs, especially Cayley graph, also automorphism
of group and automorphism of graph, we can show that 𝐺 is
graphically abelian if and only if all of its Cayley subsets are normal, 𝐺
is balanced group, and each element of 𝐺
is either fixed or inverted by conjugation. Furthermore, if 𝐺
is graphically abelian group, and let 𝑎,𝑏∈𝐺
be a pair of noncommuting elements, then 〈𝑎,𝑏〉
is Quarternion group.
Penulis: Michelle Purwagani,
Inna Kuswandari, Yayuk Wahyuni
Kode Jurnal: jpmatematikadd130071
