commutator subgroup

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commutator subgroup

[′käm·yə‚tād·ər ′səb‚grüp]

(mathematics)

The subgroup of a given group G consisting of all products of the form g₁ g₂… g_n, where each g_i is the commutator of some pair of elements in G.

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perfect group

References in periodicals archive ?

Borovoi, Abelianization of the second nonabelian Galois cohomology, Duke Math.

On some Hasse principles for algebraic groups over global fields

In [3], the authors provide a combinatorial method for calculating the abelianization of the discrete fundamental group of the permutahedron, which in turn gives a purely combinatorial method of calculating the Betti number of [M.

At each step in the truncation process, the number of generators of the abelianization of the discrete fundamental group increases, going from trivial in the case of the n-simplex to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for the associahedron and [2.

The discrete fundamental group of the associahedron

Discrete groups that are Kazhdan groups have finite abelianization [BdlHV08, Corollary 1.