How To Use Abelian group In A Sentence
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Gauss in 1801 was to take Euler's work much further and gives a considerable amount of work on modular arithmetic which amounts to a fair amount of theory of abelian groups.
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All Hirsch's publications were in group theory, in addition to the work on polycyclic groups he published on locally nilpotent groups and automorphism groups of torsion free abelian groups.
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Although Euler's work is, of course, not stated in group theoretic terms he does provide an example of the decomposition of an abelian group into cosets of a subgroup.
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In this paper the authors define a dual graph of a finite group and classify the finite non-abelian groups with dual graphs without triangles.
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In the same year he generalised von Neumann's spectral theorem to locally compact abelian groups.
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In 1925 he proved the Krull-Schmidt theorem for decomposing abelian groups of operators.
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In his talk Steinitz introduced an algebra over the ring of integers whose base elements are isomorphism classes of finite abelian groups.
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Although Euler's work is, of course, not stated in group theoretic terms he does provide an example of the decomposition of an abelian group into cosets of a subgroup.
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In 1925 he proved the Krull-Schmidt theorem for decomposing abelian groups of operators.
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He does provide an example of the decomposition of an abelian group into cosets of a subgroup.
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After further papers on subgroups of infinite abelian groups and normal numbers he wrote a series of eight papers on Arithmetic on curves of genus 1.