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Quotient Rings of Subgroup Algebras
Author(s) -
Hannah John
Publication year - 1978
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/blms/10.1.81
Subject(s) - mathematics , quotient , subring , invertible matrix , normal subgroup , conjecture , combinatorics , finite group , pure mathematics , discrete mathematics , group (periodic table) , ring (chemistry) , chemistry , organic chemistry
Suppose Q(KG) and Q(KH) are the maximal right quotient rings of the group algebras KG and KH (respectively), H being a normal subgroup of G . Brown, Lawrence and Louden have suggested the following: Conjecture . The subring of Q(KG) generated by Q(KH) and KG coincides with Q(KG) if and only if either (i) H has finite index in G , or (ii) G/H is locally finite and both Q(KH) and Q(KG) are Artinian classical quotient rings. They have proved this in three cases where KG is countable. We prove it in the case where KG is nonsingular and G/H is locally finite.