Q.3 Pick out the true statements Let Hand K be subgroups of a group G For...

Transcribed Image Text:

Q.3 Pick out the true statements Let Hand K be subgroups of a group G For g = G, define the coset HgK = {hgk|he H, k = K}. Then if H is normal, we have HgH = gH vg = G. Let GL (n, C) be the group of all nxn invertible matrices with complex entries. The set of all nxn invertible upper triangular matrices is a normal subgroup. Let M(n,R) denote the set of all nxn matrices with real entries and GL(n,R) denote the group of invertible matrices. Let G be a group of GL(n,R). Define H = {4=G|36:[0,1] →G continuous such that (0) = 4, 6(1)=1}. Then, H is a normal subgroup of G. None of these Q.3 Pick out the true statements Let Hand K be subgroups of a group G For g = G, define the coset HgK = {hgk|he H, k = K}. Then if H is normal, we have HgH = gH vg = G. Let GL (n, C) be the group of all nxn invertible matrices with complex entries. The set of all nxn invertible upper triangular matrices is a normal subgroup. Let M(n,R) denote the set of all nxn matrices with real entries and GL(n,R) denote the group of invertible matrices. Let G be a group of GL(n,R). Define H = {4=G|36:[0,1] →G continuous such that (0) = 4, 6(1)=1}. Then, H is a normal subgroup of G. None of these

Answer rating: 100% (QA)

The detailed ... View the full answer