Open AccessConstruction of multiplicative groups in modular arithmetic
Author(s) -
Purwanto Purwanto
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1872/1/012009
Subject(s) - multiplicative function , mathematics , modular arithmetic , modulo , arithmetic , multiplicative group , prime (order theory) , multiplication (music) , sequence (biology) , integer (computer science) , group (periodic table) , prime number , arithmetic function , set (abstract data type) , modular design , discrete mathematics , combinatorics , algorithm , computer science , cryptography , chemistry , organic chemistry , biology , genetics , operating system , mathematical analysis , programming language
There are multiplicative groups in modular arithmetic. It is known that when n is a positive integer, the set of all positive integers less than and relative prime to n is a group under multiplication modulo n. Some authors have studied multiplicative groups in modular arithmetic, and many of these groups have been constructed. In this paper we review some of the constructions, including constructions using elements of a geometric sequence and elements of an arithmetic sequence. Some of the constructions are extensions of the existing groups, and some others are new constructions. We also show that it is possible to find other new constructions.