3. In each part, find the order of the given element in the given group. (a) i= √-1 in the multiplicative group of nonzero complex numbers (C*, .). (1 is the identity element.) (b) in the group (R, +). (c) (1,2,2) in Z2 × Z3 × Z4 (d) (1,2,3,4) (5, 6, 7, 8, 9, 10) (written in cycle notation) in S10
3. In each part, find the order of the given element in the given group. (a) i= √-1 in the multiplicative group of nonzero complex numbers (C*, .). (1 is the identity element.) (b) in the group (R, +). (c) (1,2,2) in Z2 × Z3 × Z4 (d) (1,2,3,4) (5, 6, 7, 8, 9, 10) (written in cycle notation) in S10
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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Transcribed Image Text:3. In each part, find the order of the given element in the given group.
(a) i = √-1 in the multiplicative group of nonzero complex numbers (C*,.). (1 is the identity element.)
V
(b) in the group (R, +).
(c) (1,2,2) in Z2 × Z3 × Z4
(d) (1,2,3,4) (5, 6, 7, 8, 9, 10) (written in cycle notation) in S10
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