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On the Loewy structure of the projective indecomposable representations of some stabilizer subgroups of A(8) in characteristic 2
Title
On the Loewy structure of the projective indecomposable representations of some stabilizer subgroups of A(8) in characteristic 2.
Creator
Hindman, Peter Blake, Florida Atlantic University, Klingler, Lee
Abstract/Description
Given a module over a ring for which the Jordan-Holder theorem is valid, the Loewy series is a filtration on the composition factors of the module yielding information on the structure in which they are arranged in the module. We derive subgroups of A8 by considering stabilizers of n-tuples derived from partitions of eight letters, and develop their representation theory over a field of characteristic 2, relying heavily on methods of passing information to groups from their subgroups, with...
Show moreGiven a module over a ring for which the Jordan-Holder theorem is valid, the Loewy series is a filtration on the composition factors of the module yielding information on the structure in which they are arranged in the module. We derive subgroups of A8 by considering stabilizers of n-tuples derived from partitions of eight letters, and develop their representation theory over a field of characteristic 2, relying heavily on methods of passing information to groups from their subgroups, with special attention toward obtaining the Loewy structure of their projective indecomposable representations.
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Date Issued
1993
PURL
http://purl.flvc.org/fcla/dt/14971
Subject Headings
Representations of groups, Projective modules (Algebra), Indecomposable modules
Format
Document (PDF)
Subgroups of bounded Abelian groups
Title
Subgroups of bounded Abelian groups.
Creator
Petroro, Carla., Florida Atlantic University, Schmidmeier, Markus
Abstract/Description
Birkhoff raised the question of how to determine "relative invariants of subgroups" of a given group. Let us consider pairs (A, B ) where B is a finite pn-bounded Abelian group and A is a subgroup of B. Maps between pairs (A, B) --> (A', B') are morphisms f : B --> B' such that f (A) --> A'. Classification of such pairs, up to isomorphism, is Birkhoff's famous problem. By the Krull-Remak-Schmidt theorem, an arbitrary pair (A, B) is a direct sum of indecomposable pairs, and the multiplicities...
Show moreBirkhoff raised the question of how to determine "relative invariants of subgroups" of a given group. Let us consider pairs (A, B ) where B is a finite pn-bounded Abelian group and A is a subgroup of B. Maps between pairs (A, B) --> (A', B') are morphisms f : B --> B' such that f (A) --> A'. Classification of such pairs, up to isomorphism, is Birkhoff's famous problem. By the Krull-Remak-Schmidt theorem, an arbitrary pair (A, B) is a direct sum of indecomposable pairs, and the multiplicities of the indecomposables are determined uniquely. The purpose of this thesis is to describe the decomposition of such pairs, (A, B), explicitly for n = 2 and n = 3. We describe explicitly how an indecomposable pair can possibly embed into a given pair (A, B). This construction gives rise to formulas for the multiplicity of an indecomposable in the direct sum decomposition of the pair (A, B). These decomposition numbers form a full set of relative invariant, as requested by Birkhoff.
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Date Issued
2004
PURL
http://purl.flvc.org/fcla/dt/13118
Subject Headings
Abelian groups, Modules (Algebra), Indecomposable modules, Representations of groups, Algebras, Linear
Format
Document (PDF)