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3) Let G be a cyclic group then a) Z(G) = G,where Z(G)is the center of b) Every subgroup of G is a normal subgroup. c) All above.

3) Let G be a cyclic group then a) Z(G) = G,where Z(G)is the center of b) Every subgroup of G is a normal subgroup. c) All above.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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3- * 3) Let G be a cyclic group then a) Z(G) = G, where Z(G)is the center of G. b) Every subgroup of G is a normal subgroup. c) All above. a O b 4- * 4) Let G = Z and Ha subgroup of G defind as H = {7n, n € Z},then a) = (H+0,H + 1,H + 2,H + 3,H + 4} b) = {H + 0,H + 1,H + 2,H + 3, H + 4,H + 5, H + 6} c) = (H+0,H + 1} a C
Transcribed Image Text:3- * 3) Let G be a cyclic group then a) Z(G) = G, where Z(G)is the center of G. b) Every subgroup of G is a normal subgroup. c) All above. a O b 4- * 4) Let G = Z and Ha subgroup of G defind as H = {7n, n € Z},then a) = (H+0,H + 1,H + 2,H + 3,H + 4} b) = {H + 0,H + 1,H + 2,H + 3, H + 4,H + 5, H + 6} c) = (H+0,H + 1} a C
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