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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:Let G be a finite group and F a field. We show that all G-codes over F are
abelian if the order of G is less than 24, but for F = ℤ5 and G = S4 there exist
non-abelian G-codes over F, answering to an open problem posed in [J. J. Bernal,
Á. del Río and J. J. Simón, An intrinsical description of group codes, Des.
Codes Cryptogr.51(3) (2009) 289–300]. This problem is related to the
decomposability of a group as the product of two abelian subgroups. We consider
this problem in the case of p-groups, finding the minimal order for which all
p-groups of such order are decomposable. Finally, we study if the fact that all
G-codes are abelian remains true when the base field is changed.