Question

Consider G=(Z₂₀∗,×).

(A) List The Elements Of G.
(B) Let H={1,3,7,9}. Write Down A Multiplication Table For This Subset Of G.

Answer 1

The elements of group G=(Z₂₀*, ×) are {1, 3, 7, 9, 11, 13, 17, 19}. Subset H consists of {1, 3, 7, 9}, and its multiplication table under modulo 20 multiplication has been provided showing the results of the multiplication of the elements of H with each other.

Step-by-step explanation:

Elements of G and the Multiplication Table for H

The question involves the mathematical concepts of groups and specifically the group theory aspect of abstract algebra. Group G is denoted as G=(Z₂₀*, ×), where Z₂₀* is the set of non-zero elements of modulo 20 under multiplication.

(A) The elements of G are all integers from 1 to 19 that are relatively prime to 20, meaning they have no common factors with 20 other than 1. These elements are:

• 1, 3, 7, 9, 11, 13, 17, 19

(B) Set H is a subset of G consisting of elements {1, 3, 7, 9}. The multiplication table for this subset is as follows:

×137911379339177719399731

Note that the multiplication is modulo 20.