Algebra subgroup

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Definition

Suppose G is the algebra group corresponding to an associative algebra N (that admits an algebra group) over a field F, i.e., G = 1 + N. A subgroup H of G is termed an algebra subgroup of G if H = 1 + M for some subalgebra M of N.

Note that any algebra subgroup of an algebra group becomes an algebra group in its own right.

Facts