In (Z,+) find <{12,18}>in (S9 , composition) find <{1347) , (28)}> and <(1347)(28)>in (S9 , composition ) find <{145) , (297863)}> and <(145)(297863)> in (S9, composition) find <{135) , (2748)}> and <(135)(2748)> The image appears to contain a mathematical problem regarding permutations and group theory. The text is as follows:1. In $(\mathbb{Z}, +)$ find $\langle 12, 18 \rangle$.2. In $(S_9, \circ)$ find $\langle (1347), (28) \rangle$, and $\langle (1347)(28) \rangle$.3. In $(S_9, \circ)$ find $\langle (145), (297863) \rangle$, and $\langle (145)(297863) \rangle$.4. In $(S_9, \circ)$ find $\langle (135), (2748) \rangle$, and $\langle (135)(2748) \rangle$.Explanation:- $(\mathbb{Z}, +)$ refers to the set of integers under addition.- $(S_9, \circ)$ refers to the symmetric group on 9 elements under composition of permutations.- The notation $\langle a, b \rangle$ suggests finding the subgroup generated by the elements $a$ and $b$.- The numbers in parentheses (e.g., $(1347)$) represent cycles in permutation notation.This exercise involves understanding subgroup generation within specified groups.

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Answered: In (Z,+) find <{12,18}>.

Math

Advanced Math

In (Z,+) find <{12,18}>.

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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Topic Video

Question

In (Z,+) find <{12,18}>

in (S_{9 , composition) find <{1347) , (28)}> and <(1347)(28)>}

_in (S₉_{, composition ) find <{145) , (297863)}> and <(145)(297863)>}

_{in (}S_{9, composition) find <{135) , (2748)}> and <(135)(2748)>}

The image appears to contain a mathematical problem regarding permutations and group theory. The text is as follows:

1. In $(\mathbb{Z}, +)$ find $\langle 12, 18 \rangle$.

2. In $(S_9, \circ)$ find $\langle (1347), (28) \rangle$, and $\langle (1347)(28) \rangle$.

3. In $(S_9, \circ)$ find $\langle (145), (297863) \rangle$, and $\langle (145)(297863) \rangle$.

4. In $(S_9, \circ)$ find $\langle (135), (2748) \rangle$, and $\langle (135)(2748) \rangle$.

Explanation:

- $(\mathbb{Z}, +)$ refers to the set of integers under addition.
- $(S_9, \circ)$ refers to the symmetric group on 9 elements under composition of permutations.
- The notation $\langle a, b \rangle$ suggests finding the subgroup generated by the elements $a$ and $b$.
- The numbers in parentheses (e.g., $(1347)$) represent cycles in permutation notation.

This exercise involves understanding subgroup generation within specified groups.

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