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Is G abelian? Why or why not? What is G|? Which element of G is the identity?

Is G abelian? Why or why not? What is G|? Which element of G is the identity?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer the following three questions:

**Is \( G \) abelian? Why or why not?** **What is \( |G| \)?** **Which element of \( G \) is the identity?**
Transcribed Image Text:**Is \( G \) abelian? Why or why not?** **What is \( |G| \)?** **Which element of \( G \) is the identity?**
Consider the group \( G = \{ a, b, c, x, y, z \} \) with the binary operation depicted in the Cayley table below. (For instance, the table shows that \( aa = z \) and \( ab = x \)). \[ \begin{array}{c|cccccc} G & a & b & c & x & y & z \\ \hline a & z & x & b & c & a & y \\ b & c & y & a & z & b & x \\ c & x & z & y & a & c & b \\ x & b & a & z & y & x & c \\ y & a & b & c & x & y & z \\ z & y & c & x & b & z & a \\ \end{array} \]
Transcribed Image Text:Consider the group \( G = \{ a, b, c, x, y, z \} \) with the binary operation depicted in the Cayley table below. (For instance, the table shows that \( aa = z \) and \( ab = x \)). \[ \begin{array}{c|cccccc} G & a & b & c & x & y & z \\ \hline a & z & x & b & c & a & y \\ b & c & y & a & z & b & x \\ c & x & z & y & a & c & b \\ x & b & a & z & y & x & c \\ y & a & b & c & x & y & z \\ z & y & c & x & b & z & a \\ \end{array} \]
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