Show that there exists a non trivial normal subgroup of a group of order pq, where p and q are prime integers. Find the exact order of a non- abelian group of order less than 75 having no nontrivial normal subgroup by showing that any even ordered group G with |G| = 2n, n odd integer always has a normal subgroup H with |G : H| = 2 using regular representation of G.

Show that there exists a non trivial normal subgroup of a group of order pq, where p and q are prime integers. Find the exact order of a non- abelian group of order less than 75 having no nontrivial normal subgroup by showing that any even ordered group G with |G| = 2n, n odd integer always has a normal subgroup H with |G : H| = 2 using regular representation of G.

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 17E

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