Subgroups Flashcards
1
Q
T or F
The associative law holds in every group.
A
T
2
Q
T or F
There may be a group in which the cancellation law fails
A
F
3
Q
T or F
Every group is a subgroup of itself.
A
T
4
Q
T or F
Every group has exactly two improper subgroups.
A
F
5
Q
T or F
In every cyclic group, every element is a generator.
A
F
6
Q
T or F
A cyclic group has a unique generator.
A
F
7
Q
T or F
Every set of numbers that is a group under addition is also a group under multiplication.
A
F
8
Q
T or F
A subgroup may be defined as a subset of a group.
A
F
9
Q
T or F
Z4 is a cyclic group.
A
T
10
Q
T or F
Every subset of every group is a subgroup under the induced operation.
A
F
