On double covers of the generalized alternating group $ℤ_d ≀ _m$ as Galois groups over algebraic number fields

Martin Epkenhans

On double covers of the generalized alternating group

ℤ_{d} ≀_{m}

as Galois groups over algebraic number fields

Martin Epkenhans

Acta Arithmetica, Tome 80 (1997), p. 129-145 / Harvested from The Polish Digital Mathematics Library

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Résumé

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 $.$

Publié le : 1997-01-01

Zbl 0881.12003

EUDML-ID : urn:eudml:doc:207085

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     author = {Martin Epkenhans},
     title = {On double covers of the generalized alternating group $Z\_d [?] \_m$ as Galois groups over algebraic number fields},
     journal = {Acta Arithmetica},
     volume = {80},
     year = {1997},
     pages = {129-145},
     zbl = {0881.12003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav82i2p129bwm}
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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, Tome 80 (1997) pp. 129-145. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav82i2p129bwm/

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