Galois realizability of groups of orders p 5 and p 6

Ivo Michailov

Open Mathematics (2013)

  • Volume: 11, Issue: 5, page 910-923
  • ISSN: 2391-5455

Abstract

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Let p be an odd prime and k an arbitrary field of characteristic not p. We determine the obstructions for the realizability as Galois groups over k of all groups of orders p 5 and p 6 that have an abelian quotient obtained by factoring out central subgroups of order p or p 2. These obstructions are decomposed as products of p-cyclic algebras, provided that k contains certain roots of unity.

How to cite

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Ivo Michailov. "Galois realizability of groups of orders p 5 and p 6." Open Mathematics 11.5 (2013): 910-923. <http://eudml.org/doc/269247>.

@article{IvoMichailov2013,
abstract = {Let p be an odd prime and k an arbitrary field of characteristic not p. We determine the obstructions for the realizability as Galois groups over k of all groups of orders p 5 and p 6 that have an abelian quotient obtained by factoring out central subgroups of order p or p 2. These obstructions are decomposed as products of p-cyclic algebras, provided that k contains certain roots of unity.},
author = {Ivo Michailov},
journal = {Open Mathematics},
keywords = {Embedding problem; Galois group; p-group; Quaternion algebra; Cyclic algebra; embedding problem; -group; quaternion algebra; cyclic algebra},
language = {eng},
number = {5},
pages = {910-923},
title = {Galois realizability of groups of orders p 5 and p 6},
url = {http://eudml.org/doc/269247},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Ivo Michailov
TI - Galois realizability of groups of orders p 5 and p 6
JO - Open Mathematics
PY - 2013
VL - 11
IS - 5
SP - 910
EP - 923
AB - Let p be an odd prime and k an arbitrary field of characteristic not p. We determine the obstructions for the realizability as Galois groups over k of all groups of orders p 5 and p 6 that have an abelian quotient obtained by factoring out central subgroups of order p or p 2. These obstructions are decomposed as products of p-cyclic algebras, provided that k contains certain roots of unity.
LA - eng
KW - Embedding problem; Galois group; p-group; Quaternion algebra; Cyclic algebra; embedding problem; -group; quaternion algebra; cyclic algebra
UR - http://eudml.org/doc/269247
ER -

References

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