Union-related crimes involving great female friends abroad? (8)

I believe the answer is:

bigamies

I'm a little stuck... Click here to teach me more about this clue!

'union-related crimes' is the definition.
I can't judge whether this defines the answer.

'great female friends abroad?' is the wordplay.
I cannot really understand how this works, but
'great' could be 'big' (synonyms) and 'big' is found in the answer.
This may be the basis of clue (or it may be nonsense).

'involving' acts as a link.

Can you help me to learn more?

I've seen this clue in The Telegraph.

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