Q.2 a). If G is an abelian group that contains a pair of cyclic subgroups of order 2, show that G must contain a subgroup of order .4. Does this subgroup have to be cyclic? b) Find the centre of .D8. What about the centre ofD,0 ? What is the centre of Dn?

Q.2 a). If G is an abelian group that contains a pair of cyclic subgroups of order 2, show that G must contain a subgroup of order .4. Does this subgroup have to be cyclic? b) Find the centre of .D8. What about the centre ofD,0 ? What is the centre of Dn?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 15E: Let H1 and H2 be cyclic subgroups of the abelian group G, where H1H2=0. Prove that H1H2 is cyclic if...

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Q.2 a). If G is an abelian group that contains a pair of cyclic subgroups of
order 2, show that G must contain a subgroup of order .4. Does this
subgroup have to be cyclic?
b) Find the centre of D8. What about the centre ofD,o ? What is the
centre of D,?

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