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A Book of Abstract Algebra

Charles C. Pinter

Chapter 7

GROUPS OF PERMUTATIONS - all with Video Answers

Educators


Section 1

A

01:47

Problem 1

Consider the following permutations $f, g$, and $h$ in $S_{6}$ :
$$
\begin{gathered}
f=\left(\begin{array}{llllll}
1 & 2 & 3 & 4 & 5 & 6 \\
6 & 1 & 3 & 5 & 4 & 2
\end{array}\right) \quad g=\left(\begin{array}{llllll}
1 & 2 & 3 & 4 & 5 & 6 \\
2 & 3 & 1 & 6 & 5 & 4
\end{array}\right) \\
h=\left(\begin{array}{llllll}
1 & 2 & 3 & 4 & 5 & 6 \\
5 & 1 & 6 & 4 & 5 & 2
\end{array}\right)
\end{gathered}
$$
Compute the following:
$f^{-1}=\left(\begin{array}{cccccc}1 & 2 & 3 & 4 & 5 & 6 \\ & & & & & \end{array}\right) \quad g^{-1}=\left(\begin{array}{cccccc}1 & 2 & 3 & 4 & 5 & 6 \\ & & & & & \end{array}\right)$
$h^{-1}=\left(\begin{array}{llllll}1 & 2 & 3 & 4 & 5 & 6 \\ & & & & & \end{array}\right)$
$f \circ g=\left(\begin{array}{cccccc}1 & 2 & 3 & 4 & 5 & 6 \\ \vdots & & & & \end{array}\right) \quad g \circ f=\left(\begin{array}{llllll}1 & 2 & 3 & 4 & 5 & 6\end{array}\right)$

Taha T
Taha T
Numerade Educator
01:03

Problem 2

$$
f \circ(g \circ h)=
$$

Sanchit Jain
Sanchit Jain
Numerade Educator
01:57

Problem 3

$$
g \circ h^{-1}=
$$

Rakvi .
Rakvi .
Numerade Educator
01:01

Problem 4

$$
h \cdot g^{-1} a f^{-1}=
$$

Raj Bala
Raj Bala
Numerade Educator
01:03

Problem 5

$$
g \circ g \circ g=
$$

Sanchit Jain
Sanchit Jain
Numerade Educator