(4). Suppose that f: G→ G' is a monomorphism, G is a non-trivial group and G' is non-abelian. Then G can not be abelian. (5). If every subgroup of G is a finite group, then G must be a finite group. (6). Let Z14 acts on a set X with 3 elements. Then there are at least 2 orbits under the action.
(4). Suppose that f: G→ G' is a monomorphism, G is a non-trivial group and G' is non-abelian. Then G can not be abelian. (5). If every subgroup of G is a finite group, then G must be a finite group. (6). Let Z14 acts on a set X with 3 elements. Then there are at least 2 orbits under the action.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.6: Quotient Groups
Problem 37E: Let H and K be arbitrary groups and let HK denotes the Cartesian product of H and K: HK=(h,k)hHandkK...
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