Dihedral Group in The Ancient Genetic

Abstract

The standard genetic code consist of four nucleotide bases which encode genes to produce amino acids needed by living things. The addition of new base  (Dummy) causes a sequence of bases to become five nucleotide bases called ancient genetic codes. The five base set is denoted by , where B forms group through matching , , , , and   from set . Ancient genetic codes can be reviewed as algebraic structures as a vector spaces and other structures as symmetry groups. In this article, discussed the properties of symmetry groups from ancient genetic codes that will produce dihedral groups. The study began by constructing an expanded nucleotide base isomorphism with . The presence of base  causes  to have a cardinality of 24, denoted as  with .  isomorphic with  which is denoted by . Group  had three clasess of partitions based on strong-weak, purin-pyrimidin types, and amino-keto nucleotide groups which are denoted as , , and . All three classes are subgroups of . By using the rules of rotation and reflection in the four-side plane, it was found that only one group fulfilled the rule was named the dihedral group.