The abstract group $G$ simply isomorphic with the alternating group on six letters
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چکیده
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The group of alternating colored permutations is the natural analogue of the classical alternating group, inside the wreath product Zr ≀Sn. We present a ‘Coxeterlike’ presentation for this group and compute the length function with respect to that presentation. Then, we present this group as a covering of Z r 2 ≀ Sn and use this point of view to give another expression for the length function. ...
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Let An ⊆ Sn denote the alternating and the symmetric groups on 1, . . . , n. MacMahaon’s theorem [11], about the equi-distribution of the length and the major indices in Sn, has received far reaching refinements and generalizations, by Foata [5], Carlitz [3, 4], FoataSchützenberger [6], Garsia-Gessel [7] and followers. Our main goal is to find analogous statistics and identities for the alterna...
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We exhibit an example of Hendrik Lenstra of an expansive automorphism on a compact connected abelian group K such that its homoclinic group is not isomorphic to the Pontryagin duaî K.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1903
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1903-00996-3