On additive bases II

Weidong Gao; Dongchun Han; Guoyou Qian; Yongke Qu; Hanbin Zhang

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Covering locally compact groups by less than $2^{ω}$ many translates of a compact nullset

Márton Elekes, Árpád Tóth (2007)

Fundamenta Mathematicae

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Gruenhage asked if it was possible to cover the real line by less than continuum many translates of a compact nullset. Under the Continuum Hypothesis the answer is obviously negative. Elekes and Stepr mans gave an affirmative answer by showing that if $C_{E K}$ is the well known compact nullset considered first by Erdős and Kakutani then ℝ can be covered by cof() many translates of $C_{E K}$ . As this set has no analogue in more general groups, it was asked by Elekes and Stepr mans whether such a result...

A note on a class of factorized $p$ -groups

Enrico Jabara (2005)

Czechoslovak Mathematical Journal

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In this note we study finite $p$ -groups $G = A B$ admitting a factorization by an Abelian subgroup $A$ and a subgroup $B$ . As a consequence of our results we prove that if $B$ contains an Abelian subgroup of index $p^{n - 1}$ then $G$ has derived length at most $2 n$ .

Compact Abelian groups and extensions of Haar measures

A. Hulanicki

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ContentsIntroduction.................................................................................................................... 31. Preliminaries (topology measure).................................................................... 32. Problems and the theorem.................................................................................... 73. Preliminaries (abstract groups, Cartesian products)....................................... 94. Preliminaries (automorphisms, duality...

On sequences over a finite abelian group with zero-sum subsequences of forbidden lengths

Weidong Gao, Yuanlin Li, Pingping Zhao, Jujuan Zhuang (2016)

Colloquium Mathematicae

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Let G be an additive finite abelian group. For every positive integer ℓ, let $d i s c_{ℓ} (G)$ be the smallest positive integer t such that each sequence S over G of length |S| ≥ t has a nonempty zero-sum subsequence of length not equal to ℓ. In this paper, we determine $d i s c_{ℓ} (G)$ for certain finite groups, including cyclic groups, the groups $G = C ₂ \oplus C_{2 m}$ and elementary abelian 2-groups. Following Girard, we define disc(G) as the smallest positive integer t such that every sequence S over G with |S| ≥ t has nonempty zero-sum...

Regularity of sets with constant intrinsic normal in a class of Carnot groups

Marco Marchi (2014)

Annales de l’institut Fourier

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In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type $☆$ ” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type $☆$ is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano...

The Erdős-Heilbronn problem for finite groups

Paul Balister, Jeffrey Paul Wheeler (2009)

Acta Arithmetica

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On absolutely-nilpotent of class $k$ groups

Patrizia Longobardi, Trueman MacHenry, Mercede Maj, James Wiegold (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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A group $G$ in a variety $V$ is said to be absolutely- $V$ , and we write $G \in A V$ , if central extensions by $G$ are again in $V$ . Absolutely-abelian groups have been classified by F. R. Beyl. In this paper we concentrate upon the class $A N_{k}$ of absolutely-nilpotent of class $k$ groups. We prove some closure properties of the class $A N_{k}$ and we show that every nilpotent of class $k$ group can be embedded in an $A N_{k}$ -gvoup. We describe all metacyclic $A N_{k}$ -groups and we characterize $2$ -generator and infinite $3$ -generator $A N_{2}$ -groups....

On zero-symmetric nearrings with identity whose additive groups are simple

Wen-Fong Ke, Johannes H. Meyer, Günter F. Pilz, Gerhard Wendt (2024)

Czechoslovak Mathematical Journal

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We investigate conditions on an infinite simple group in order to construct a zero-symmetric nearring with identity on it. Using the Higman-Neumann-Neumann extensions and Clay’s characterization, we obtain zero-symmetric nearrings with identity with the additive groups infinite simple groups. We also show that no zero-symmetric nearring with identity can have the symmetric group $Sym (ℕ)$ as its additive group.

Some remarks on Lorenzen $r$ -group of partly ordered groups

Jiří Močkoř, Angeliki Kontolatou (1996)

Czechoslovak Mathematical Journal

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О $p$ -группах автоморфизмов абелевых $p$ -групп

Е.И. Хухро (2000)

Algebra i Logika

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