So, subspaces of vector spaces, and subgroups of groups, are not allowed to be empty.(adsbygoogle = window.adsbygoogle || []).push({});

This is because "there exists an identity element". We could include the empty set in these substructures but have the definition otherwise unchanged.

I'm curious as to what the consequences of such would be. If the empty subset of a group G were considered a subgroup of G, what would be some consequences in our important theorems?

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# The exclusion of empty substructures

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