5. Prove (using the subgroup condition rather than using the axioms) that the seta b0 сER}H1= {( 8 6 ) : 0: a, cЄR*, bЄR‚cЄR*,bЄRis a subgroup of GL2(R)

To prove that the set H={(a0bc):a,c∈R∗,b∈R} is a subgroup of GL2(R), we will use the subgroup…

Answered: 5. Prove (using the subgroup condition…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

Problem 4E: 4. Prove that the special linear group is a normal subgroup of the general linear group .

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5. Prove (using the subgroup condition rather than using the axioms) that the set a b 0 с ER} H 1= {( 8 6 ) : 0 : a, cЄR*, bЄR ‚cЄR*,bЄR is a subgroup of GL2(R)

5. Prove (using the subgroup condition rather than using the axioms) that the set a b 0 с ER} H 1= {( 8 6 ) : 0 : a, cЄR, bЄR ‚cЄR,bЄR is a subgroup of GL2(R)