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A Torsion Projective Class for a Group Algebra
Author(s) -
Leary Ian J.
Publication year - 2000
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609399006566
Subject(s) - mathematics , quotient , torsion (gastropod) , dihedral group , cyclic group , brauer group , isomorphism (crystallography) , schur multiplier , combinatorics , dicyclic group , dihedral angle , group (periodic table) , order (exchange) , pure mathematics , algebra over a field , non abelian group , abelian group , crystallography , medicine , hydrogen bond , chemistry , crystal structure , surgery , organic chemistry , finance , molecule , economics
Let G be the group given by the following presentation: [formula] The subgroup generated by ab is infinite‐cyclic and normal, with quotient the dihedral group of order 6, so G is cyclic‐by‐finite. The subgroups H = 〈 a , c 〉 and K = 〈 b , c 〉 are both dihedral of order 6, and G is isomorphic to the free product of H and K amalgamating L = H ∩ K . We study K 0 ( kG ), the Grothendieck group of isomorphism classes of finitely generated projective kG ‐modules, and, in particular, the dependence of K 0 ( kG ) on the choice of field k . As usual, let Q, R and C stand for the rationals, reals and complex numbers, respectively. We prove the following. 1991 Mathematics Subject Classification 19A31, 16S34, 55N15.