Indecomposable (1,3)-groups and a matrix problem

David M. Arnold; Adolf Mader; Otto Mutzbauer; Ebru Solak

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 2, page 307-355
  • ISSN: 0011-4642

Abstract

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Almost completely decomposable groups with a critical typeset of type ( 1 , 3 ) and a p -primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient p k , either no indecomposables if k ≤ 2 ; only six near isomorphism types of indecomposables if k = 3 ; and indecomposables of arbitrary large rank if k ≥ 4 .

How to cite

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Arnold, David M., et al. "Indecomposable (1,3)-groups and a matrix problem." Czechoslovak Mathematical Journal 63.2 (2013): 307-355. <http://eudml.org/doc/260716>.

@article{Arnold2013,
abstract = {Almost completely decomposable groups with a critical typeset of type $(1,3)$ and a $p$-primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient $p^k$, either no indecomposables if $k\le 2$; only six near isomorphism types of indecomposables if $k=3$; and indecomposables of arbitrary large rank if $k\ge 4$.},
author = {Arnold, David M., Mader, Adolf, Mutzbauer, Otto, Solak, Ebru},
journal = {Czechoslovak Mathematical Journal},
keywords = {almost completely decomposable group; indecomposable; representation; almost completely decomposable groups; finite rank torsion-free Abelian groups; subgroups of finite index; regulating subgroups; near-isomorphism classes; indecomposable groups},
language = {eng},
number = {2},
pages = {307-355},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Indecomposable (1,3)-groups and a matrix problem},
url = {http://eudml.org/doc/260716},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Arnold, David M.
AU - Mader, Adolf
AU - Mutzbauer, Otto
AU - Solak, Ebru
TI - Indecomposable (1,3)-groups and a matrix problem
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 2
SP - 307
EP - 355
AB - Almost completely decomposable groups with a critical typeset of type $(1,3)$ and a $p$-primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient $p^k$, either no indecomposables if $k\le 2$; only six near isomorphism types of indecomposables if $k=3$; and indecomposables of arbitrary large rank if $k\ge 4$.
LA - eng
KW - almost completely decomposable group; indecomposable; representation; almost completely decomposable groups; finite rank torsion-free Abelian groups; subgroups of finite index; regulating subgroups; near-isomorphism classes; indecomposable groups
UR - http://eudml.org/doc/260716
ER -

References

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