The rank 2 geometries of the simple Suzuki groups .
Leemans, Dimitri (1998)
Beiträge zur Algebra und Geometrie
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Leemans, Dimitri (1998)
Beiträge zur Algebra und Geometrie
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For a finitely generated group, we study the relations between its rank, the maximal rank of its free quotient, called co-rank (inner rank, cut number), and the maximal rank of its free abelian quotient, called the Betti number. We show that any combination of the group's rank, co-rank, and Betti number within obvious constraints is realized for some finitely presented group (for Betti number equal to rank, the group can be chosen torsion-free). In addition, we show that the Betti number...
A. Lachlan (1974)
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We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.