- #1
mathmari
Gold Member
MHB
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Hey!
I have to determine whether the following sentences are correct or not.
Could you give me some hints for the ones with the question mark?? (Blush)
I have to determine whether the following sentences are correct or not.
- Any two groups with three elements are isomorphic.
- At any cyclic group, each element is a generator.
- Each cyclic group has at least one non trivial proper subgroup.
- The group
with respect to the multiplication is isomorphic to .
- Each cyclic group is abelian.
- An abelian group can have a non-abelian subgroup.
- For each
there is an abelian group with order .
- For each
there is a non-abelian group with order .
- True, since the multiplicative table is the same with the only difference the symbols.
- False, for example the group
is cyclic with generator . , so is not a generator of .
- ?
- The multiplication table of the group
with respect to the multiplication is : and the multiplication table of the group is
The tables are the same, the only difference is the symbols ( )
- True!
- ?
- ?
- ?
Could you give me some hints for the ones with the question mark?? (Blush)