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4. The group defined by the following table is called the group of quaternions. Use the table to determine each of the following. a. The center b. cl(a) c. cl(b) d. All cyclic subgroups e a a² a³ b ba ba² ba³ e e a a² b ba ba² ba³ a a a³ e ba ba² ba³ b a² a² a³ e a ba² ba³ b ba a³ e a a² ba³ b ba ba² b b ba³ ba² ba a² a e a³ ba ba b ba³ ba² a³ a² a e ba² ba³ ba² ba³ ba ba² b ba ba³ b e a³ a² a a e a³ a²

4. The group defined by the following table is called the group of quaternions. Use the table to determine each of the following. a. The center b. cl(a) c. cl(b) d. All cyclic subgroups e a a² a³ b ba ba² ba³ e e a a² b ba ba² ba³ a a a³ e ba ba² ba³ b a² a² a³ e a ba² ba³ b ba a³ e a a² ba³ b ba ba² b b ba³ ba² ba a² a e a³ ba ba b ba³ ba² a³ a² a e ba² ba³ ba² ba³ ba ba² b ba ba³ b e a³ a² a a e a³ a²

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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4. The group defined by the following table is called the group of quaternions. Use the table to determine each of the following. a. The center b. cl(a) c. cl(b) d. All cyclic subgroups e a a² a³ b ba ba² ba³ e e a a² a³ b ba ba² ba³ a a a² a³ e ba ba² ba³ b a² a² a³ e a ba² ba³ b ba a³ a³ e a a² ba³ b ba ba² b b ba³ ba² ba a² a e a³ ba ba b ba³ ba² a³ a² a e ba² ba³ ba² ba³ ba ba² b ba ba³ b e a³ a² a a e a³ a²
Transcribed Image Text:4. The group defined by the following table is called the group of quaternions. Use the table to determine each of the following. a. The center b. cl(a) c. cl(b) d. All cyclic subgroups e a a² a³ b ba ba² ba³ e e a a² a³ b ba ba² ba³ a a a² a³ e ba ba² ba³ b a² a² a³ e a ba² ba³ b ba a³ a³ e a a² ba³ b ba ba² b b ba³ ba² ba a² a e a³ ba ba b ba³ ba² a³ a² a e ba² ba³ ba² ba³ ba ba² b ba ba³ b e a³ a² a a e a³ a²
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