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[Groups and Symmetries] How do you solve Q3, thanks
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- Let A={ a,b,c }. Prove or disprove that P(A) is a group with respect to the operation of union. (Sec. 1.1,7c)15. Prove that if for all in the group , then is abelian.Prove that each of the following subsets H of GL(2,C) is subgroup of the group GL(2,C), the general linear group of order 2 over C a. H={ [ 1001 ],[ 1001 ],[ 1001 ],[ 1001 ] } b. H={ [ 1001 ],[ i00i ],[ i00i ],[ 1001 ] }
- 18. If is a subgroup of the group such that for all left cosets and of in, prove that is normal in.Suppose G1 and G2 are groups with normal subgroups H1 and H2, respectively, and with G1/H1 isomorphic to G2/H2. Determine the possible orders of H1 and H2 under the following conditions. a. G1=24 and G2=18 b. G1=32 and G2=4015. Prove that each of the following subsets of is subgroup of the group ,the general linear group of order over. a. b. c. d.