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Let H be a non-empty subset of a group G. Then H is a  subgroup of G iff      a,b∈H⇒ab\power{-1}∈H, where b\power{-1} is the inverse of b in G.

Let H be a non-empty subset of a group G. Then H is a  subgroup of G iff      a,b∈H⇒ab\power{-1}∈H, where b\power{-1} is the inverse of b in G.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.3: Subgroups
Problem 43E: 43. Suppose that is a nonempty subset of a group . Prove that is a subgroup of if and only if for...
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Let H be a non-empty subset of a group G. Then H is a
 subgroup of G iff
     a,b∈H⇒ab\power{-1}∈H, where b\power{-1} is the inverse of b in G.

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