hsong9 said:The Attempt at a Solution
A. I know |g^2| = 20/2 = 10 and |g^5| = 20/5 = 4
But |g^8|, |g^3| don't know..
B. a)H=<a^d> , right?
but
I don't know how to solve b) and c)
Thanks!
|g| represents the order or number of elements in the group G. In this case, it means that there are 20 elements in the group G.
Subgroup H is defined as the group generated by the elements x and y. This means that H contains all possible combinations of x and y, including their inverses, and the identity element.
To solve problems involving group G and subgroup H, you need to first understand the properties and structure of both G and H. Then, you can use techniques such as Lagrange's Theorem or the Coset Enumeration Method to determine the number of elements and structure of H within G.
Solving problems involving groups and subgroups has applications in various fields, such as mathematics, physics, and computer science. It allows us to understand and analyze complex structures and systems, as well as make predictions and solve real-world problems.
Some common challenges when solving group problems include understanding the properties and structure of the group and subgroup, identifying the correct techniques to use, and determining the appropriate level of abstraction to approach the problem. It may also involve complex calculations and the need for a deep understanding of abstract algebra.