Section 5 True or False
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A cyclic group has a unique generator.
False
A subgroup may be defined as a subset of a group.
False
Every group has exactly two improper subgroups.
False
Every set of numbers that is a group under addition is also a group under multiplication.
False
Every subset of every group is a subgroup under the induced operation.
False
In every cyclic group, every element is a generator.
False
There may be a group in which the cancellation law fails.
False
Every group is a subgroup of itself.
True
The associative law holds in every group.
True
Z_4 is a cyclic group.
True
