direct product

noun Mathematics.
a group, or other such system, every element of which can be written uniquely as the product of elements of disjoint groups, with each group contributing one element to the product.

1920–25 Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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The evidence must reflect that the statement was spontaneous, excited, or impulsive as a direct product of the event itself.
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