Hw6 Problem 3

Return to Homework 6, Glossary, Theorems

Problem 3

Show that $\mathbb{Z}_p$ has no proper subgroups if p is prime.


We know that the orders of the subgroups of $\mathbb{Z}_p$ are the divisor of p by the Theorem of Lagrange.
However, p is prime, whose divisor are 1 and p. So $\mathbb{Z}_p$ has no proper subgroups and only has trivial subgroup and improper subgroup.

Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License