An approach to decomposability of a class of almost completely decomposable groups

Date

2024-6-27

Author

Kocabıyık, Makbule

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A torsion-free abelian group G is completely decomposable of finite rank if G is isomorphic to a finite direct sum of subgroups of Q and almost completely decomposable if G contains a completely decomposable subgroup R with G/R a finite group.The regulator R(G) is intersection of all regulating subgroups of G and is a completely decomposable subgroup of finite index in G. The isomorphism types of the regulator R(G) and the regulator quotient G/R(G) are near-isomorphism invariants of an almost completely decomposable group G. In this thesis we consider a special case. Let p be a prime, (1, 2) = (t1, t2, t3) be a set of types, partially ordered as t1 is not comparable with t2 and t3 and t2 < t3 . An almost completely decomposable G with critical typeset (1, 2) and a regulating index a p-power is called a p-local (1, 2)-group. For p-local (1, 2)-groups, the main question is to determine the near isomorphism classes of indecomposable (1, 2)-groups.

Subject Keywords

Almost completely decomposable groups, Torsion free groups, Decomposability of almost completely decomposable groups.

URI

https://hdl.handle.net/11511/110053

Collections

Graduate School of Natural and Applied Sciences, Thesis