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Let 3 denote the centre of a group G. then show that a 3 iff N(a) = G. also show that if G is finite, then a € 3 iff o(N(a)) = o(G)

Let 3 denote the centre of a group G. then show that a 3 iff N(a) = G. also show that if G is finite, then a € 3 iff o(N(a)) = o(G)

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.4: Cyclic Groups
Problem 33E: If G is a cyclic group, prove that the equation x2=e has at most two distinct solutions in G.
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Let 3 denote the centre of a group G. then show that a = 3 iff N(a) = G. also show that if G is finite, then a ≤ 3 iff o(N(a)) = o(G).
Transcribed Image Text:Let 3 denote the centre of a group G. then show that a = 3 iff N(a) = G. also show that if G is finite, then a ≤ 3 iff o(N(a)) = o(G).
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