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All Journal Jurnal Eurekamatika Prosiding Seminar Nasional Sisfotek (Sistem Informasi dan Teknologi Informasi) Media Abdimas
Binastya Anggara Sekti
Universitas Esa Unggul
Humanities Computer Science & IT Health Professions Industrial & Manufacturing Engineering Library & Information Science Mathematics Public Health Social Sciences Other

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Journal : Jurnal Eurekamatika

 1 
A Note on Relative Normal Subgroups Yudi Mahatma; Ibnu Hadi; Binastya Anggara Sekti
Jurnal EurekaMatika Vol 11, No 1 (2023): Jurnal Eurekamatika
Publisher : Universitas Pendidikan Indonesia (UPI)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17509/jem.v11i1.56092

Abstract

Let G be finite group and α∈Aut(G). In 2016, Ganjali and Erfanian introduced the notion of a normal subgroup of G which is relative to α, called the α-normal subgroup. In detail, N is an α-normal subgroup of G if for every g∈G and n∈N we have g^(-1) nα(g)∈N. In this research, we show that if N is an α-normal subgroup of G and τ∈Aut(G) then N is τ-normal in G if and only if α(g)τ(g^(-1) )∈N for every g∈G.Keywords: Group, Normal subgroup, α-normal subgroup.AbstrakMisalkan G grup hingga dan α∈Aut(G). Tahun 2016, Ganjali dan Erfanian memperkenalkan ide tentang suatu subgrup normal dari G relatif terhadap α, dinamakan subgrup normal-α. Secara rinci, N adalah suatu subgrup normal-α dari G apabila untuk setiap g∈G dan n∈N berlaku g^(-1) nα(g)∈N. Dalam penelitian ini diperlihatkan bahwa jika N adalah suatu subgrup normal-α dari G dan τ∈Aut(G) maka N normal-τ di G jika dan hanya jika α(g)τ(g^(-1) )∈N untuk setiap g∈G.
Co-Authors Alivia Yulfitri Andri Kurnia Maulana Euis Sadeli Ibnu Hadi Ichwani, arief Ilham Banuaji Lista Meria Nizirwan Anwar Tri Ismardiko Ummanah Ummanah Widodo, Agung Mulyo Yanathifal Salsabila Anggraeni Yudi Mahatma