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Using Parallelize with my own function

Dear Group,

I have a problem with Parallelize. I have defined the following

In[1]:= CyclicGroupQ[G_] := MemberQ[GroupOrder[PermutationGroup[{#}]]
& /@ GroupElements[G],  GroupOrder[G]].

In[2]:= DistributeDefinitions[CyclicGroupQ]
Out[2]= {CyclicGroupQ}

This function gives True if G is cyclic, False otherwise. If I try to
use Parallelize with this function I get the following message:

In[3]:= Parallelize[CyclicGroupQ[SymmetricGroup[5]]]

Parallelize::nopar1: CyclicGroupQ[SymmetricGroup[5]] cannot be
parallelized; proceeding with sequential evaluation.

Out[3]= False

However, if I use Parallelize with the definition of the function, I
do not get this message:

In[4]:= Parallelize[ MemberQ[GroupOrder[PermutationGroup[{#}]] & /@
GroupElements[SymmetricGroup[5]], GroupOrder[SymmetricGroup[5]]]]

Out[4]= False

How could I make my function parallelizable?

Adam Lelkes

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