Displaying similar documents to “On the increasing solutions of the translation equation”

On Meager Additive and Null Additive Sets in the Cantor Space 2 ω and in ℝ

Tomasz Weiss (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let T be the standard Cantor-Lebesgue function that maps the Cantor space 2 ω onto the unit interval ⟨0,1⟩. We prove within ZFC that for every X 2 ω , X is meager additive in 2 ω iff T(X) is meager additive in ⟨0,1⟩. As a consequence, we deduce that the cartesian product of meager additive sets in ℝ remains meager additive in ℝ × ℝ. In this note, we also study the relationship between null additive sets in 2 ω and ℝ.

The superfocal subgroup

Marian Deaconescu (1984)

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

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Nel presente lavoro vengono dimostrati teoremi d'esistenza di p -complementi normali nei gruppi finiti.

On TI-subgroups and QTI-subgroups of finite groups

Ruifang Chen, Xianhe Zhao (2020)

Czechoslovak Mathematical Journal

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Let G be a group. A subgroup H of G is called a TI-subgroup if H H g = 1 or H for every g G and H is called a QTI-subgroup if C G ( x ) N G ( H ) for any 1 x H . In this paper, a finite group in which every nonabelian maximal is a TI-subgroup (QTI-subgroup) is characterized.

Sums of reciprocals of additive functions running over short intervals

J.-M. De Koninck, I. Kátai (2007)

Colloquium Mathematicae

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Letting f(n) = A log n + t(n), where t(n) is a small additive function and A a positive constant, we obtain estimates for the quantities x n x + H 1 / f ( Q ( n ) ) and x p x + H 1 / f ( Q ( p ) ) , where H = H(x) satisfies certain growth conditions, p runs over prime numbers and Q is a polynomial with integer coefficients, whose leading coefficient is positive, and with all its roots simple.

A note on the super-additive and sub-additive transformations of aggregation functions: The multi-dimensional case

Fateme Kouchakinejad, Alexandra Šipošová (2017)

Kybernetika

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For an aggregation function A we know that it is bounded by A * and A * which are its super-additive and sub-additive transformations, respectively. Also, it is known that if A * is directionally convex, then A = A * and A * is linear; similarly, if A * is directionally concave, then A = A * and A * is linear. We generalize these results replacing the directional convexity and concavity conditions by the weaker assumptions of overrunning a super-additive function and underrunning a sub-additive function, respectively. ...

On the Behavior of Power Series with Completely Additive Coefficients

Oleg Petrushov (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

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Consider the power series ( z ) = n = 1 α ( n ) z , where α(n) is a completely additive function satisfying the condition α(p) = o(lnp) for prime numbers p. Denote by e(l/q) the root of unity e 2 π i l / q . We give effective omega-estimates for ( e ( l / p k ) r ) when r → 1-. From them we deduce that if such a series has non-singular points on the unit circle, then it is a zero function.

More remarks on the intersection ideal 𝒩

Tomasz Weiss (2018)

Commentationes Mathematicae Universitatis Carolinae

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We prove in ZFC that every 𝒩 additive set is 𝒩 additive, thus we solve Problem 20 from paper [Weiss T., A note on the intersection ideal 𝒩 , Comment. Math. Univ. Carolin. 54 (2013), no. 3, 437-445] in the negative.

Strong measure zero and meager-additive sets through the prism of fractal measures

Ondřej Zindulka (2019)

Commentationes Mathematicae Universitatis Carolinae

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We develop a theory of sharp measure zero sets that parallels Borel’s strong measure zero, and prove a theorem analogous to Galvin–Mycielski–Solovay theorem, namely that a set of reals has sharp measure zero if and only if it is meager-additive. Some consequences: A subset of 2 ω is meager-additive if and only if it is -additive; if f : 2 ω 2 ω is continuous and X is meager-additive, then so is f ( X ) .

Ulm-Kaplansky invariants of S(KG)/G

P. V. Danchev (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let G be an infinite abelian p-group and let K be a field of the first kind with respect to p of characteristic different from p such that s p ( K ) = or s p ( K ) = 0 . The main result of the paper is the computation of the Ulm-Kaplansky functions of the factor group S(KG)/G of the normalized Sylow p-subgroup S(KG) in the group ring KG modulo G. We also characterize the basic subgroups of S(KG)/G by proving that they are isomorphic to S(KB)/B, where B is a basic subgroup of G.

On quotients of the space of orderings of the field ℚ(x)

Paweł Gładki, Bill Jacob (2016)

Banach Center Publications

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In this paper we present a method of obtaining new examples of spaces of orderings by considering quotient structures of the space of orderings ( X ( x ) , G ( x ) ) - it is, in general, nontrivial to determine whether, for a subgroup G G ( x ) the derived quotient structure ( X ( x ) | G , G ) is a space of orderings, and we provide some insights into this problem. In particular, we show that if a quotient structure arising from a subgroup of index 2 is a space of orderings, then it necessarily is a profinite one.

Finite groups with some SS-supplemented subgroups

Mengling Jiang, Jianjun Liu (2021)

Czechoslovak Mathematical Journal

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A subgroup H of a finite group G is said to be SS-supplemented in G if there exists a subgroup K of G such that G = H K and H K is S-quasinormal in K . We analyze how certain properties of SS-supplemented subgroups influence the structure of finite groups. Our results improve and generalize several recent results.

On weakly-supplemented subgroups of finite groups

Qingjun Kong (2019)

Czechoslovak Mathematical Journal

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A subgroup H of a finite group G is weakly-supplemented in G if there exists a proper subgroup K of G such that G = H K . In this paper, some interesting results with weakly-supplemented minimal subgroups to a smaller subgroup of G are obtained.

Connected transversals -- the Zassenhaus case

Tomáš Kepka, Petr Němec (2000)

Commentationes Mathematicae Universitatis Carolinae

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In this short note, it is shown that if A , B are H -connected transversals for a finite subgroup H of an infinite group G such that the index of H in G is at least 3 and H H u H v = 1 whenever u , v G H and u v - 1 G H then A = B is a normal abelian subgroup of G .

Large free subgroups of automorphism groups of ultrahomogeneous spaces

Szymon Głąb, Filip Strobin (2015)

Colloquium Mathematicae

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We consider the following notion of largeness for subgroups of S . A group G is large if it contains a free subgroup on generators. We give a necessary condition for a countable structure A to have a large group Aut(A) of automorphisms. It turns out that any countable free subgroup of S can be extended to a large free subgroup of S , and, under Martin’s Axiom, any free subgroup of S of cardinality less than can also be extended to a large free subgroup of S . Finally, if Gₙ are countable...

Notes on the average number of Sylow subgroups of finite groups

Jiakuan Lu, Wei Meng, Alexander Moretó, Kaisun Wu (2021)

Czechoslovak Mathematical Journal

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We show that if the average number of (nonnormal) Sylow subgroups of a finite group is less than 29 4 then G is solvable or G / F ( G ) A 5 . This generalizes an earlier result by the third author.