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Exercises: 1) Let G = (Z6,O) .Show which of the following subsets of G is a subgroup of it? a) H = {0,2}ls b) K = {0,3} c) L = {0,2,4} 2) Let G = V4 .Show which of the following subsets of G is a subgroup of it? a) H = {e, a} b) K = {e,b} c) L = {e,c} d) M = {e,b,c} %3D bun %3D odi on %3D LAnaitie %3D %3D botonab bre s9 botomb bre nsbno otmita sd ot biea ris %3D ad + 0}. Prove that H < G? .quognod 0 19. boll %3D %3D 4) Let G = (Q*,.) and H = {2",n E Z}. Prove that H < G? 5) Try to find all subgroups of all groups we are study in lecture 1 and 2 %3D I-aalea W quoy oiloraqs 1o siboiog Dal lla t (n)0 b Ils not ()0 bn S= (1-)0 = = (-),1-= A=00-1-0)1-=0).1--0),1= AF (-0 1=-),1= -),1-0-).-D vW quoig oiborego iboieg al DD He tol ()0 bm1. (+,) = 3 9. 100 2920 OWI SVerd ow n is onby I (0)0 0 = bo atintai zed tromslo viinobi oru tsoxs 0 ni momolo yrsvo o2sosd quog siboiag 16-tlesin lo (K) w (A.0)9)=0 bus R nitoi

Exercises: 1) Let G = (Z6,O) .Show which of the following subsets of G is a subgroup of it? a) H = {0,2}ls b) K = {0,3} c) L = {0,2,4} 2) Let G = V4 .Show which of the following subsets of G is a subgroup of it? a) H = {e, a} b) K = {e,b} c) L = {e,c} d) M = {e,b,c} %3D bun %3D odi on %3D LAnaitie %3D %3D botonab bre s9 botomb bre nsbno otmita sd ot biea ris %3D ad + 0}. Prove that H < G? .quognod 0 19. boll %3D %3D 4) Let G = (Q*,.) and H = {2",n E Z}. Prove that H < G? 5) Try to find all subgroups of all groups we are study in lecture 1 and 2 %3D I-aalea W quoy oiloraqs 1o siboiog Dal lla t (n)0 b Ils not ()0 bn S= (1-)0 = = (-),1-= A=00-1-0)1-=0).1--0),1= AF (-0 1=-),1= -),1-0-).-D vW quoig oiborego iboieg al DD He tol ()0 bm1. (+,) = 3 9. 100 2920 OWI SVerd ow n is onby I (0)0 0 = bo atintai zed tromslo viinobi oru tsoxs 0 ni momolo yrsvo o2sosd quog siboiag 16-tlesin lo (K) w (A.0)9)=0 bus R nitoi

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Exercises: 1) Let G = (Z6,O) .Show which of the following subsets of G is a subgroup of it? a) H = {0,2}ls b) K = {0,3} c) L = {0,2,4} 2) Let G = V4 .Show which of the following subsets of G is a subgroup of it? a) H = {e, a} b) K = {e,b} c) L = {e,c} d) M = {e,b,c} %3D bun %3D odi on %3D LAnaitie %3D %3D botonab bre s9 botomb bre nsbno otmita sd ot biea ris %3D ad + 0}. Prove that H < G? .quognod 0 19. boll %3D %3D 4) Let G = (Q*,.) and H = {2",n E Z}. Prove that H < G? 5) Try to find all subgroups of all groups we are study in lecture 1 and 2 %3D I-aalea W quoy oiloraqs 1o siboiog Dal lla t (n)0 b Ils not ()0 bn S= (1-)0 = = (-),1-= A=00-1-0)1-=0).1--0),1= AF (-0 1=-),1= -),1-0-).-D vW quoig oiborego iboieg al DD He tol ()0 bm1. (+,) = 3 9. 100 2920 OWI SVerd ow n is onby I (0)0 0 = bo atintai zed tromslo viinobi oru tsoxs 0 ni momolo yrsvo o2sosd quog siboiag 16-tlesin lo (K) w (A.0)9)=0 bus R nitoi
Transcribed Image Text:Exercises: 1) Let G = (Z6,O) .Show which of the following subsets of G is a subgroup of it? a) H = {0,2}ls b) K = {0,3} c) L = {0,2,4} 2) Let G = V4 .Show which of the following subsets of G is a subgroup of it? a) H = {e, a} b) K = {e,b} c) L = {e,c} d) M = {e,b,c} %3D bun %3D odi on %3D LAnaitie %3D %3D botonab bre s9 botomb bre nsbno otmita sd ot biea ris %3D ad + 0}. Prove that H < G? .quognod 0 19. boll %3D %3D 4) Let G = (Q*,.) and H = {2",n E Z}. Prove that H < G? 5) Try to find all subgroups of all groups we are study in lecture 1 and 2 %3D I-aalea W quoy oiloraqs 1o siboiog Dal lla t (n)0 b Ils not ()0 bn S= (1-)0 = = (-),1-= A=00-1-0)1-=0).1--0),1= AF (-0 1=-),1= -),1-0-).-D vW quoig oiborego iboieg al DD He tol ()0 bm1. (+,) = 3 9. 100 2920 OWI SVerd ow n is onby I (0)0 0 = bo atintai zed tromslo viinobi oru tsoxs 0 ni momolo yrsvo o2sosd quog siboiag 16-tlesin lo (K) w (A.0)9)=0 bus R nitoi
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