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Let G be set of all 2 x 2 matrices in GL2 (Z5) of the form (i) Show that G is a subgroup of GL2 (Z5). (ii) Find the order of G. (iii) Is G a normal subgroup of GL2 (Z5)? (²2), (iv) Let N be the subset of all matrices in G of the form normal subgroup of G. (v) Show that the factor group G/N is cyclic of order 4. (9) with c, d E Z5 and d = 0. with ce Z5. Show that N is a

Let G be set of all 2 x 2 matrices in GL2 (Z5) of the form (i) Show that G is a subgroup of GL2 (Z5). (ii) Find the order of G. (iii) Is G a normal subgroup of GL2 (Z5)? (²2), (iv) Let N be the subset of all matrices in G of the form normal subgroup of G. (v) Show that the factor group G/N is cyclic of order 4. (9) with c, d E Z5 and d = 0. with ce Z5. Show that N is a

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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Let G be set of all 2 × 2 matrices in GL2 (Z5) of the form (i) Show that G is a subgroup of GL2(Z5). (ii) Find the order of G. (iii) Is G a normal subgroup of GL2 (Z5)? 0 (2). (iv) Let N be the subset of all matrices in G of the form normal subgroup of G. (v) Show that the factor group G/N is cyclic of order 4. (19) with c, d e Z5 and d 0. with ce Z5. Show that N is a
Transcribed Image Text:Let G be set of all 2 × 2 matrices in GL2 (Z5) of the form (i) Show that G is a subgroup of GL2(Z5). (ii) Find the order of G. (iii) Is G a normal subgroup of GL2 (Z5)? 0 (2). (iv) Let N be the subset of all matrices in G of the form normal subgroup of G. (v) Show that the factor group G/N is cyclic of order 4. (19) with c, d e Z5 and d 0. with ce Z5. Show that N is a
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