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*if A is an additive subgroup of the additive group B and G is B-magic then G is A-magic*

In general, I know what a converse is. But I'm having trouble figuring out what the converse of this statement is. The literal converse, as far as I can tell, does not make any sense.

*if*

*G is A-magic, then*

*A is an additive subgroup of the additive group B and G is B-magic*(i.e., Who said anything about B?). Is there an accepted convention about converses when you have a compound antecedent, like you do here?