   Chapter 3.1, Problem 1TFE

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Textbook Problem
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# Label each of the following statements as either true or false.The set ℤ of all integers is a nonabelian group with respect to subtraction.

To determine

Whether the statement, “The set of all integers is a non-abelian group with respect to subtraction” is true or false.

Explanation

Explanation:

Definition of a group:

Suppose the binary operation is defined for element of set G. The G is a group with respect to provided the following conditions hold:

1. G is closed under . That is xG and yG imply that xy is in G.

2. is associative. For all x,y,z in G, x(yz)=(xy)z.

3. G has an identity element e. There is an e in G such that xe=ex=x for all xG.

4. G contains inverses. For each aG, there exists bG such that ab=ba=e.

Condition for an abelian group:

G is called commutative group or an abelian group, if is commutative

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