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Question 2. The subgroup generated by S could have been defined a second way, as the set of all possible products of elements in S. Indeed, if g, and g2 are two elements in a subgroup of G then closure implies that the products (gi), (g2), (gig2)², (gig2)(g₁)³ (8182) (81)³(182) (g2)¹2, etc..... must also be in the subgroup. Define the closure of S to be the set: 5 = {ss sne Z,n ≥ 0 and s, ES, a, = ±1 for each 1 ≤ i ≤ n} and prove that (S) = S.

Question 2. The subgroup generated by S could have been defined a second way, as the set of all possible products of elements in S. Indeed, if g, and g2 are two elements in a subgroup of G then closure implies that the products (gi), (g2), (gig2)², (gig2)(g₁)³ (8182) (81)³(182) (g2)¹2, etc..... must also be in the subgroup. Define the closure of S to be the set: 5 = {ss sne Z,n ≥ 0 and s, ES, a, = ±1 for each 1 ≤ i ≤ n} and prove that (S) = S.

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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Question 2. The subgroup generated by S could have been defined a second way, as the set of all possible products of elements in S. Indeed, if g and g2 are two elements in a subgroup of G then closure implies that the products (gi), (g2). (gig₁)², (gig2)(g₁)³ (9₁2) (₁)³ (₁2) (₂)¹2, etc..... must also be in the subgroup. Define the closure of S to be the set: ... S = {sissne Z,n ≥ 0 and s; E S, a, = ±1 for each 1 ≤ i ≤ n} and prove that (S) = S.
Transcribed Image Text:Question 2. The subgroup generated by S could have been defined a second way, as the set of all possible products of elements in S. Indeed, if g and g2 are two elements in a subgroup of G then closure implies that the products (gi), (g2). (gig₁)², (gig2)(g₁)³ (9₁2) (₁)³ (₁2) (₂)¹2, etc..... must also be in the subgroup. Define the closure of S to be the set: ... S = {sissne Z,n ≥ 0 and s; E S, a, = ±1 for each 1 ≤ i ≤ n} and prove that (S) = S.
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