QI. Examine whether or not the following listed subsets form a subgroup. (write all details) 1. H, = {e, (1432), (1234), (13) • (24)}. 2. H2 = {0,4,8,12,16,20,24,28,32}, 3. H3 = {r, r3, l4,l3}, from the group (P4.9). from the group (Z36, +36) from the group of symmetric (S3,9) 4. H4 = { ),a, b,c € R, a + 0 + c (lower bound)} from the group of %3D %3D %3D %3D non-singular matrices (M2x2 (R) x). 5. H5 = {x € G: x? = x}, from the abelian group (G,+).
QI. Examine whether or not the following listed subsets form a subgroup. (write all details) 1. H, = {e, (1432), (1234), (13) • (24)}. 2. H2 = {0,4,8,12,16,20,24,28,32}, 3. H3 = {r, r3, l4,l3}, from the group (P4.9). from the group (Z36, +36) from the group of symmetric (S3,9) 4. H4 = { ),a, b,c € R, a + 0 + c (lower bound)} from the group of %3D %3D %3D %3D non-singular matrices (M2x2 (R) x). 5. H5 = {x € G: x? = x}, from the abelian group (G,+).
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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Transcribed Image Text:Q1. Examine whether or not the following listed subsets form a subgroup. (write
all details)
1. H, = {e, (1432), (1234), (13) • (24)},
2. H2 = {0,4,8,12,16,20,24,28,32},
3. H3 = {r, r3, l4,l3),
from the group (P,).
from the group (Z36, +36)
from the group of symmetric (S3,0)
%3D
4. H4 = { ),a, b,c € R, a + 0 # c (lower bound)} from the group of
non-singular matrices (M2x2 (R) X).
5. Hg = {x € G: x? = x}, from the abelian group (G,+).
%3D
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