Displaying similar documents to “Presentations of finite simple groups: a computational approach”

On the topology of polynomials with bounded integer coefficients

De-Jun Feng (2016)

Journal of the European Mathematical Society

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For a real number q > 1 and a positive integer m , let Y m ( q ) : = i = 0 n ϵ i q i : ϵ i 0 , ± 1 , ... , ± m , n = 0 , 1 , ... . In this paper, we show that Y m ( q ) is dense in if and only if q < m + 1 and q is not a Pisot number. This completes several previous results and answers an open question raised by Erdös, Joó and Komornik [8].

Groups of given intermediate word growth

Laurent Bartholdi, Anna Erschler (2014)

Annales de l’institut Fourier

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We show that there exists a finitely generated group of growth f for all functions f : + + satisfying f ( 2 R ) f ( R ) 2 f ( η + R ) for all R large enough and η + 2 . 4675 the positive root of X 3 - X 2 - 2 X - 4 . Set α - = log 2 / log η + 0 . 7674 ; then all functions that grow uniformly faster than exp ( R α - ) are realizable as the growth of a group. We also give a family of sum-contracting branched groups of growth exp ( R α ) for a dense set of α [ α - , 1 ] .

L p inequalities for the growth of polynomials with restricted zeros

Nisar A. Rather, Suhail Gulzar, Aijaz A. Bhat (2022)

Archivum Mathematicum

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Let P ( z ) = ν = 0 n a ν z ν be a polynomial of degree at most n which does not vanish in the disk | z | < 1 , then for 1 p < and R > 1 , Boas and Rahman proved P ( R z ) p ( R n + z p / 1 + z p ) P p . In this paper, we improve the above inequality for 0 p < by involving some of the coefficients of the polynomial P ( z ) . Analogous result for the class of polynomials P ( z ) having no zero in | z | > 1 is also given.

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...

On the divisor function over Piatetski-Shapiro sequences

Hui Wang, Yu Zhang (2023)

Czechoslovak Mathematical Journal

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Let [ x ] be an integer part of x and d ( n ) be the number of positive divisor of n . Inspired by some results of M. Jutila (1987), we prove that for 1 < c < 6 5 , n x d ( [ n c ] ) = c x log x + ( 2 γ - c ) x + O x log x , where γ is the Euler constant and [ n c ] is the Piatetski-Shapiro sequence. This gives an improvement upon the classical result of this problem.

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.

On unit group of finite semisimple group algebras of non-metabelian groups up to order 72

Gaurav Mittal, Rajendra Kumar Sharma (2021)

Mathematica Bohemica

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We characterize the unit group of semisimple group algebras 𝔽 q G of some non-metabelian groups, where F q is a field with q = p k elements for p prime and a positive integer k . In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group ( ( C 3 × C 3 ) C 3 ) C 2 of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.

Global analytic and Gevrey surjectivity of the Mizohata operator D 2 + i x 2 2 k D 1

Lamberto Cattabriga, Luisa Zanghirati (1990)

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

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The surjectivity of the operator D 2 + i x 2 2 k D 1 from the Gevrey space E s R 2 , s 1 , onto itself and its non-surjectivity from E s R 3 to E s R 3 is proved.

Limits of relatively hyperbolic groups and Lyndon’s completions

Olga Kharlampovich, Alexei Myasnikov (2012)

Journal of the European Mathematical Society

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We describe finitely generated groups H universally equivalent (with constants from G in the language) to a given torsion-free relatively hyperbolic group G with free abelian parabolics. It turns out that, as in the free group case, the group H embeds into the Lyndon’s completion G [ t ] of the group G , or, equivalently, H embeds into a group obtained from G by finitely many extensions of centralizers. Conversely, every subgroup of G [ t ] containing G is universally equivalent to G . Since finitely...

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.

On the structural theory of  II 1 factors of negatively curved groups

Ionut Chifan, Thomas Sinclair (2013)

Annales scientifiques de l'École Normale Supérieure

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Ozawa showed in [21] that for any i.c.c. hyperbolic group, the associated group factor L Γ is solid. Developing a new approach that combines some methods of Peterson [29], Ozawa and Popa [27, 28], and Ozawa [25], we strengthen this result by showing that L Γ is strongly solid. Using our methods in cooperation with a cocycle superrigidity result of Ioana [12], we show that profinite actions of lattices in  Sp ( n , 1 ) , n 2 , are virtually W * -superrigid.