- #1

gruba

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- 1

## Homework Statement

Show that the group [itex](\mathbb Z_4,_{+4})[/itex] is isomorphic to [itex](\langle i\rangle,\cdot)[/itex]?

## Homework Equations

-Group isomorphism

## The Attempt at a Solution

Let [itex]\mathbb Z_4=\{0,1,2,3\}[/itex].

[itex](\mathbb Z_4,_{+4})[/itex] can be represented using Cayley's table:

[tex]

\begin{array}{c|lcr}

{_{+4}} & 0 & 1 & 2 & 3 \\

\hline

0 & 0 & 1 & 2 & 3 \\

1 & 1 & 2 & 3 & 0 \\

2 & 2 & 3 & 0 & 1 \\

3 & 3 & 0 & 1 & 2 \\

\end{array}

[/tex]

What is the set [itex]\langle i\rangle[/itex]?

How to define [itex](\langle i\rangle,\cdot)[/itex]?