1. The problem statement, all variables and given/known data
I do not understand the following statement (Please, see the attachment):
"C4 has trivial subgroups and only one cyclic subgroup of 2 elements, namely <b>. This is because both a and c can be verified to be generators of C4."
3. The attempt at a solution
The notation <something> is normally used to indicate a generator of a group.
However, the paragraph uses the notation only for the cyclic subgroup b such that <b>.
The following support statement for the above clause is what I do not understand:
"This is because both a and c can be verified to be generators of C4."
If a subgroup has a generator, then it is a cyclic group.
The paragraph says that the group has two generators, a and c.
Then, a and c must be also cyclic subgroups of C4.
This is a contradiction to the first clause that C4 has only one generator b.
What does the paragraph really mean?
I do not understand the following statement (Please, see the attachment):
"C4 has trivial subgroups and only one cyclic subgroup of 2 elements, namely <b>. This is because both a and c can be verified to be generators of C4."
3. The attempt at a solution
The notation <something> is normally used to indicate a generator of a group.
However, the paragraph uses the notation only for the cyclic subgroup b such that <b>.
The following support statement for the above clause is what I do not understand:
"This is because both a and c can be verified to be generators of C4."
If a subgroup has a generator, then it is a cyclic group.
The paragraph says that the group has two generators, a and c.
Then, a and c must be also cyclic subgroups of C4.
This is a contradiction to the first clause that C4 has only one generator b.
What does the paragraph really mean?
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