5. Let G be a finite group. Suppose G has a subgroup H {1c} such that HCK for every nontrivial subgroup K of G. Label each of the following statements as true or false. Justify each answer with a proof or a counterexample. (a) H is a normal subgroup of G. (b) H is cyclic of prime order. (c) G must be abelian.

5. Let G be a finite group. Suppose G has a subgroup H {1c} such that HCK for every nontrivial subgroup K of G. Label each of the following statements as true or false. Justify each answer with a proof or a counterexample. (a) H is a normal subgroup of G. (b) H is cyclic of prime order. (c) G must be abelian.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.8: Some Results On Finite Abelian Groups (optional)

Problem 14E: Suppose that the abelian group G can be written as the direct sum G=C22C3C3, where Cn is a cyclic...

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