For a group G and a fixed element a ∈ G, define the subset C(a) to be the set of all elements in G that commute with a. C(a) = {g ∈ G : ag = ga} (a) Let G = D4. Find C(V ) and C(D0). (b) Let G = U(9). Find C(2) and C(7). (c) Let G = SL(2, R). Find C [1,1] [1,1] . (d) For a group G and a non-identity element a ∈ G, show that a ∈ C(a) and a −1 ∈ C(a). (e) Show that for any a in a group G, C(a) is a subset of G

For a group G and a fixed element a ∈ G, define the subset C(a) to be the set of all elements in G that commute with a. C(a) = {g ∈ G : ag = ga} (a) Let G = D4. Find C(V ) and C(D0). (b) Let G = U(9). Find C(2) and C(7). (c) Let G = SL(2, R). Find C [1,1] [1,1] . (d) For a group G and a non-identity element a ∈ G, show that a ∈ C(a) and a −1 ∈ C(a). (e) Show that for any a in a group G, C(a) is a subset of G

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 39E

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