Groups

Question 1

T or F

A group may have more than one identity element.

Answer 1

F

Question 2

T or F

Any two groups of three elements are isomorphic.

Answer 2

T

Question 3

T or F

In a group, each linear equation has a solution.

Answer 3

T

Question 4

T or F

The proper attitude toward a definition is to memorize it so that you can reproduce it word for a word as in the text.

Answer 4

F

Question 5

T or F

Any definition a person gives for a group is correct provided that everything that is a group by that person’s definition is also a group by the definition in the text.

Answer 5

F

Question 6

T or F

Any definition a person gives for a group is correct provided he or she can show that everything that satisfies the definition satisfies the one in the text and conversely.

Answer 6

T

Question 7

T or F

Every finite group of at most three elements is abelian.

Answer 7

T

Question 8

T or F

An equation of the form axb=c always has a unique solution in a group.

Answer 8

T

Question 9

T or F

The empty set can be considered a group.

Answer 9

F

Question 10

T or F

Every group is a binary algebraic structure.

Answer 10

T