Hello!

Using the external direct product , the group

is isomorphic to one (and only one!) of the following groups (this question reminds me of a game show...)

a)

b)

c)

d)

I am assuming these groups are the well known groups

are the integers modulo n under addittion

is the alternating group (all even permutations of n) under function composition

is the dihedral group of order

and is the set of permutations of n

The question recommends determining which groups it is not isomorphic to and determining the answer by elimination.

I started by the question noting that is cyclic, I believe? so it must be isomorphic to a cyclic group as well...

and also it must have the same number of elements of each order of any group it is isomorphic... but even armed with those facts I am having trouble finding that any of a), b), c) or d) are isomorphic to the given group

Any help appreciated!

Thank you!