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Displaying similar documents to “Endomorphism kernel property for finite groups”

Self-small products of abelian groups

Josef Dvořák, Jan Žemlička (2022)

Commentationes Mathematicae Universitatis Carolinae

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Let A and B be two abelian groups. The group A is called B -small if the covariant functor Hom ( A , - ) commutes with all direct sums B ( κ ) and A is self-small provided it is A -small. The paper characterizes self-small products applying developed closure properties of the classes of relatively small groups. As a consequence, self-small products of finitely generated abelian groups are described.

A property which ensures that a finitely generated hyper-(Abelian-by-finite) group is finite-by-nilpotent

Fares Gherbi, Nadir Trabelsi (2024)

Czechoslovak Mathematical Journal

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Let 𝔐 be the class of groups satisfying the minimal condition on normal subgroups and let Ω be the class of groups of finite lower central depth, that is groups G such that γ i ( G ) = γ i + 1 ( G ) for some positive integer i . The main result states that if G is a finitely generated hyper-(Abelian-by-finite) group such that for every x G , there exists a normal subgroup H x of finite index in G satisfying x , x h 𝔐 Ω for every h H x , then G is finite-by-nilpotent. As a consequence of this result, we prove that a finitely generated...

The evolution and Poisson kernels on nilpotent meta-abelian groups

Richard Penney, Roman Urban (2013)

Studia Mathematica

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Let S be a semidirect product S = N⋊ A where N is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and A is isomorphic to k , k>1. We consider a class of second order left-invariant differential operators on S of the form α = L a + Δ α , where α k , and for each a k , L a is left-invariant second order differential operator on N and Δ α = Δ - α , , where Δ is the usual Laplacian on k . Using some probabilistic techniques (e.g., skew-product formulas for diffusions on S and N respectively)...

Completely bounded lacunary sets for compact non-abelian groups

Kathryn Hare, Parasar Mohanty (2015)

Studia Mathematica

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In this paper, we introduce and study the notion of completely bounded Λ p sets ( Λ p c b for short) for compact, non-abelian groups G. We characterize Λ p c b sets in terms of completely bounded L p ( G ) multipliers. We prove that when G is an infinite product of special unitary groups of arbitrarily large dimension, there are sets consisting of representations of unbounded degree that are Λ p sets for all p < ∞, but are not Λ p c b for any p ≥ 4. This is done by showing that the space of completely bounded L p ( G ) ...

A note on infinite a S -groups

Reza Nikandish, Babak Miraftab (2015)

Czechoslovak Mathematical Journal

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Let G be a group. If every nontrivial subgroup of G has a proper supplement, then G is called an a S -group. We study some properties of a S -groups. For instance, it is shown that a nilpotent group G is an a S -group if and only if G is a subdirect product of cyclic groups of prime orders. We prove that if G is an a S -group which satisfies the descending chain condition on subgroups, then G is finite. Among other results, we characterize all abelian groups for which every nontrivial quotient group...

Number of solutions in a box of a linear equation in an Abelian group

Maciej Zakarczemny (2016)

Colloquium Mathematicae

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For every finite Abelian group Γ and for all g , a , . . . , a k Γ , if there exists a solution of the equation i = 1 k a i x i = g in non-negative integers x i b i , where b i are positive integers, then the number of such solutions is estimated from below in the best possible way.

Permutability of centre-by-finite groups

Brunetto Piochi (1989)

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

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Let G be a group and m be an integer greater than or equal to 2 . G is said to be m -permutable if every product of m elements can be reordered at least in one way. We prove that, if G has a centre of finite index z , then G is ( 1 + [ z / 2 ] ) -permutable. More bounds are given on the least m such that G is m -permutable.

The unit groups of semisimple group algebras of some non-metabelian groups of order 144

Gaurav Mittal, Rajendra K. Sharma (2023)

Mathematica Bohemica

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We consider all the non-metabelian groups G of order 144 that have exponent either 36 or 72 and deduce the unit group U ( 𝔽 q G ) of semisimple group algebra 𝔽 q G . Here, q denotes the power of a prime, i.e., q = p r for p prime and a positive integer r . Up to isomorphism, there are 6 groups of order 144 that have exponent either 36 or 72 . Additionally, we also discuss how to simply obtain the unit groups of the semisimple group algebras of those non-metabelian groups of order 144 that are a direct product of two...

Polycyclic groups with automorphisms of order four

Tao Xu, Fang Zhou, Heguo Liu (2016)

Czechoslovak Mathematical Journal

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In this paper, we study the structure of polycyclic groups admitting an automorphism of order four on the basis of Neumann’s result, and prove that if α is an automorphism of order four of a polycyclic group G and the map ϕ : G G defined by g ϕ = [ g , α ] is surjective, then G contains a characteristic subgroup H of finite index such that the second derived subgroup H ' ' is included in the centre of H and C H ( α 2 ) is abelian, both C G ( α 2 ) and G / [ G , α 2 ] are abelian-by-finite. These results extend recent and classical results in...

Almost everywhere convergence of convolution powers on compact abelian groups

Jean-Pierre Conze, Michael Lin (2013)

Annales de l'I.H.P. Probabilités et statistiques

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It is well-known that a probability measure μ on the circle 𝕋 satisfies μ n * f - f d m p 0 for every f L p , every (some) p [ 1 , ) , if and only if | μ ^ ( n ) | l t ; 1 for every non-zero n ( μ is strictly aperiodic). In this paper we study the a.e. convergence of μ n * f for every f L p whenever p g t ; 1 . We prove a necessary and sufficient condition, in terms of the Fourier–Stieltjes coefficients of μ , for the strong sweeping out property (existence of a Borel set B with lim sup μ n * 1 B = 1 a.e. and lim inf μ n * 1 B = 0 a.e.). The results are extended to general compact Abelian groups...

On the structure of sequences with forbidden zero-sum subsequences

W. D. Gao, R. Thangadurai (2003)

Colloquium Mathematicae

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We study the structure of longest sequences in d which have no zero-sum subsequence of length n (or less). We prove, among other results, that for n = 2 a and d arbitrary, or n = 3 a and d = 3, every sequence of c(n,d)(n-1) elements in d which has no zero-sum subsequence of length n consists of c(n,d) distinct elements each appearing n-1 times, where c ( 2 a , d ) = 2 d and c ( 3 a , 3 ) = 9 .

The density of representation degrees

Martin Liebeck, Dan Segal, Aner Shalev (2012)

Journal of the European Mathematical Society

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For a group G and a positive real number x , define d G ( x ) to be the number of integers less than x which are dimensions of irreducible complex representations of G . We study the asymptotics of d G ( x ) for algebraic groups, arithmetic groups and finitely generated linear groups. In particular we prove an “alternative” for finitely generated linear groups G in characteristic zero, showing that either there exists α > 0 such that d G ( x ) > x α for all large x , or G is virtually abelian (in which case d G ( x ) is bounded). ...

On a translation property of positive definite functions

Lars Omlor, Michael Leinert (2010)

Banach Center Publications

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If G is a locally compact group with a compact invariant neighbourhood of the identity e, the following property (*) holds: For every continuous positive definite function h≥ 0 with compact support there is a constant C h > 0 such that L x h · g C h h g for every continuous positive definite g≥0, where L x is left translation by x. In [L], property (*) was stated, but the above inequality was proved for special h only. That “for one h” implies “for all h” seemed obvious, but turned out not to be obvious at...

Group algebras whose groups of normalized units have exponent 4

Victor Bovdi, Mohammed Salim (2018)

Czechoslovak Mathematical Journal

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We give a full description of locally finite 2 -groups G such that the normalized group of units of the group algebra F G over a field F of characteristic 2 has exponent 4 .

Finite groups whose all proper subgroups are 𝒞 -groups

Pengfei Guo, Jianjun Liu (2018)

Czechoslovak Mathematical Journal

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A group G is said to be a 𝒞 -group if for every divisor d of the order of G , there exists a subgroup H of G of order d such that H is normal or abnormal in G . We give a complete classification of those groups which are not 𝒞 -groups but all of whose proper subgroups are 𝒞 -groups.