On double covers of the generalized alternating group ℤ d ≀ m as Galois groups over algebraic number fields

Martin Epkenhans

Acta Arithmetica (1997)

  • Volume: 82, Issue: 2, page 129-145
  • ISSN: 0065-1036

Abstract

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Let ℤ d ≀ m b e t h e g e n e r a l i z e d a l t e r n a t i n g g r o u p . W e p r o v e t h a t a l l d o u b l e c o v e r s o f ℤd ≀ m o c c u r a s G a l o i s g r o u p s o v e r a n y a l g e b r a i c n u m b e r f i e l d . W e f u r t h e r r e a l i z e s o m e o f t h e s e d o u b l e c o v e r s a s t h e G a l o i s g r o u p s o f r e g u l a r e x t e n s i o n s o f ℚ ( T ) . I f d i s o d d a n d m > 7 , t h e n e v e r y c e n t r a l e x t e n s i o n o f ℤd ≀ m o c c u r s a s t h e G a l o i s g r o u p o f a r e g u l a r e x t e n s i o n o f ℚ ( T ) . W e f u r t h e r i m p r o v e s o m e o f o u r e a r l i e r r e s u l t s c o n c e r n i n g d o u b l e c o v e r s o f t h e g e n e r a l i z e d s y m m e t r i c g r o u p ℤd ≀ m .

How to cite

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Martin Epkenhans. "On double covers of the generalized alternating group $ℤ_d ≀ _m$ as Galois groups over algebraic number fields." Acta Arithmetica 82.2 (1997): 129-145. <http://eudml.org/doc/207085>.

@article{MartinEpkenhans1997,
abstract = {Let $ℤ_d ≀ $m$ be the generalized alternating group. We prove that all double covers of $ℤd ≀ m$ occur as Galois groups over any algebraic number field. We further realize some of these double covers as the Galois groups of regular extensions of ℚ(T). If d is odd and m >7, then every central extension of $ℤd ≀ m$ occurs as the Galois group of a regular extension of ℚ(T). We further improve some of our earlier results concerning double covers of the generalized symmetric group $ℤd ≀ m$.$},
author = {Martin Epkenhans},
journal = {Acta Arithmetica},
keywords = {generalized alternating group; Galois group; algebraic number field; double covers; rational function field},
language = {eng},
number = {2},
pages = {129-145},
title = {On double covers of the generalized alternating group $ℤ_d ≀ _m$ as Galois groups over algebraic number fields},
url = {http://eudml.org/doc/207085},
volume = {82},
year = {1997},
}

TY - JOUR
AU - Martin Epkenhans
TI - On double covers of the generalized alternating group $ℤ_d ≀ _m$ as Galois groups over algebraic number fields
JO - Acta Arithmetica
PY - 1997
VL - 82
IS - 2
SP - 129
EP - 145
AB - Let $ℤ_d ≀ $m$ be the generalized alternating group. We prove that all double covers of $ℤd ≀ m$ occur as Galois groups over any algebraic number field. We further realize some of these double covers as the Galois groups of regular extensions of ℚ(T). If d is odd and m >7, then every central extension of $ℤd ≀ m$ occurs as the Galois group of a regular extension of ℚ(T). We further improve some of our earlier results concerning double covers of the generalized symmetric group $ℤd ≀ m$.$
LA - eng
KW - generalized alternating group; Galois group; algebraic number field; double covers; rational function field
UR - http://eudml.org/doc/207085
ER -

References

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