Displaying similar documents to “On the total number of principal series of a finite abelian group.”

Properties of subgroups not containing their centralizers

Lemnouar Noui (2009)

Annales mathématiques Blaise Pascal

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In this paper, we give a generalization of Baer Theorem on the injective property of divisible abelian groups. As consequences of the obtained result we find a sufficient condition for a group G to express as semi-direct product of a divisible subgroup D and some subgroup H . We also apply the main Theorem to the p -groups with center of index p 2 , for some prime p . For these groups we compute N c ( G ) the number of conjugacy classes and N a the number of abelian maximal subgroups and N n a the number...

Words and repeated factors.

Carpi, Arturo, de Luca, Aldo (1999)

Séminaire Lotharingien de Combinatoire [electronic only]

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Substitutions on two letters, cutting segments and their projections

Sierk W. Rosema (2007)

Journal de Théorie des Nombres de Bordeaux

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In this paper we study the structure of the projections of the finite cutting segments corresponding to unimodular substitutions over a two-letter alphabet. We show that such a projection is a block of letters if and only if the substitution is Sturmian. Applying the procedure of projecting the cutting segments corresponding to a Christoffel substitution twice results in the original substitution. This induces a duality on the set of Christoffel substitutions.

Palindromic complexity of infinite words associated with simple Parry numbers

Petr Ambrož, Zuzana Masáková, Edita Pelantová, Christiane Frougny (2006)

Annales de l’institut Fourier

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A simple Parry number is a real number β > 1 such that the Rényi expansion of 1 is finite, of the form d β ( 1 ) = t 1 ⋯ t m . We study the palindromic structure of infinite aperiodic words u β that are the fixed point of a substitution associated with a simple Parry number β . It is shown that the word u β contains infinitely many palindromes if and only if t 1 = t 2 = ⋯ = t m - 1 ≥ t m . Numbers β satisfying this condition are the so-called Pisot numbers. If t m = 1 then u β is an Arnoux-Rauzy word. We show that if β is a confluent Pisot number then...

Substitutions, abstract number systems and the space filling property

Clemens Fuchs, Robert Tijdeman (2006)

Annales de l’institut Fourier

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In this paper we study multi-dimensional words generated by fixed points of substitutions by projecting the integer points on the corresponding broken halfline. We show for a large class of substitutions that the resulting word is the restriction of a linear function modulo 1 and that it can be decided whether the resulting word is space filling or not. The proof uses lattices and the abstract number system associated with the substitution.

Finite groups with globally permutable lattice of subgroups

C. Bagiński, A. Sakowicz (1999)

Colloquium Mathematicae

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The notions of permutable and globally permutable lattices were first introduced and studied by J. Krempa and B. Terlikowska-Osłowska [4]. These are lattices preserving many interesting properties of modular lattices. In this paper all finite groups with globally permutable lattices of subgroups are described. It is shown that such finite p-groups are exactly the p-groups with modular lattices of subgroups, and that the non-nilpotent groups form an essentially larger class though they...