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

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

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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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.
Transcribed Image Text: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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