The Bogomolov multiplier of groups of order $p^7$ and exponent $p$

Zeinab Araghi Rostami; Mohsen Parvizi; Peyman Niroomand

Displaying similar documents to “The Bogomolov multiplier of groups of order $p^7$ and exponent $p$”

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 $L^{p} (G)$ ...

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...

Pointwise multipliers on martingale Campanato spaces

Eiichi Nakai, Gaku Sadasue (2014)

Studia Mathematica

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We introduce generalized Campanato spaces $_{p, ϕ}$ on a probability space (Ω,ℱ,P), where p ∈ [1,∞) and ϕ: (0,1] → (0,∞). If p = 1 and ϕ ≡ 1, then $_{p, ϕ} = B M O$ . We give a characterization of the set of all pointwise multipliers on $_{p, ϕ}$ .

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 $Sp (n, 1)$ , $n \geq 2$ , are virtually $W^{*}$ -superrigid.

Oscillating multipliers on the Heisenberg group

E. K. Narayanan, S. Thangavelu (2001)

Colloquium Mathematicae

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Let ℒ be the sublaplacian on the Heisenberg group Hⁿ. A recent result of Müller and Stein shows that the operator $ℒ^{- 1 / 2} s i n \sqrt ℒ$ is bounded on $L^{p} (H ⁿ)$ for all p satisfying |1/p - 1/2| < 1/(2n). In this paper we show that the same operator is bounded on $L^{p}$ in the bigger range |1/p - 1/2| < 1/(2n-1) if we consider only functions which are band limited in the central variable.

Obstruction sets and extensions of groups

Francesca Balestrieri (2016)

Acta Arithmetica

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Let X be a nice variety over a number field k. We characterise in pure “descent-type” terms some inequivalent obstruction sets refining the inclusion $X {(_{k})}^{é t, B r} \subset X {(_{k})}^{B r ₁}$ . In the first part, we apply ideas from the proof of $X {(_{k})}^{é t, B r} = X {(_{k})}^{_{k}}$ by Skorobogatov and Demarche to new cases, by proving a comparison theorem for obstruction sets. In the second part, we show that if $\subset \subset_{k}$ are such that $\subset E x t (,_{k})$ , then $X {(_{k})}^{} = X {(_{k})}^{}$ . This allows us to conclude, among other things, that $X {(_{k})}^{é t, B r} = X {(_{k})}^{_{k}}$ and $X {(_{k})}^{S o l, B r ₁} = X {(_{k})}^{S o l_{k}}$ .

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 $4$ .

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.

Continuous images of Lindelöf $p$ -groups, $σ$ -compact groups, and related results

Aleksander V. Arhangel'skii (2019)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that there exists a $σ$ -compact topological group which cannot be represented as a continuous image of a Lindelöf $p$ -group, see Example 2.8. This result is based on an inequality for the cardinality of continuous images of Lindelöf $p$ -groups (Theorem 2.1). A closely related result is Corollary 4.4: if a space $Y$ is a continuous image of a Lindelöf $p$ -group, then there exists a covering $γ$ of $Y$ by dyadic compacta such that $| γ | \leq 2^{ω}$ . We also show that if a homogeneous compact space $Y$ is...

The Ribes-Zalesskii property of some one relator groups

Gilbert Mantika, Narcisse Temate-Tangang, Daniel Tieudjo (2022)

Archivum Mathematicum

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The profinite topology on any abstract group $G$ , is one such that the fundamental system of neighborhoods of the identity is given by all its subgroups of finite index. We say that a group $G$ has the Ribes-Zalesskii property of rank $k$ , or is RZ $_{k}$ with $k$ a natural number, if any product $H_{1} H_{2} \dots H_{k}$ of finitely generated subgroups $H_{1}, H_{2}, \dots, H_{k}$ is closed in the profinite topology on $G$ . And a group is said to have the Ribes-Zalesskii property or is RZ if it is RZ $_{k}$ for any natural number $k$ . In this paper we characterize...

Characterization of the alternating groups by their order and one conjugacy class length

Alireza Khalili Asboei, Reza Mohammadyari (2016)

Czechoslovak Mathematical Journal

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Let $G$ be a finite group, and let $N (G)$ be the set of conjugacy class sizes of $G$ . By Thompson’s conjecture, if $L$ is a finite non-abelian simple group, $G$ is a finite group with a trivial center, and $N (G) = N (L)$ , then $L$ and $G$ are isomorphic. Recently, Chen et al. contributed interestingly to Thompson’s conjecture under a weak condition. They only used the group order and one or two special conjugacy class sizes of simple groups and characterized successfully sporadic simple groups (see Li’s PhD dissertation)....

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...

An $M_{q} ()$ -functional calculus for power-bounded operators on certain UMD spaces

Earl Berkson, T. A. Gillespie (2005)

Studia Mathematica

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For 1 ≤ q < ∞, let $_{q} ()$ denote the Banach algebra consisting of the bounded complex-valued functions on the unit circle having uniformly bounded q-variation on the dyadic arcs. We describe a broad class ℐ of UMD spaces such that whenever X ∈ ℐ, the sequence space ℓ²(ℤ,X) admits the classes $_{q} ()$ as Fourier multipliers, for an appropriate range of values of q > 1 (the range of q depending on X). This multiplier result expands the vector-valued Marcinkiewicz Multiplier Theorem in the direction...

Permutability of centre-by-finite groups

Brunetto Piochi (1989)

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

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Product decompositions of quasirandom groups and a Jordan type theorem

Nikolay Nikolov, László Pyber (2011)

Journal of the European Mathematical Society

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We first note that a result of Gowers on product-free sets in groups has an unexpected consequence: If $k$ is the minimal degree of a representation of the finite group $G$ , then for every subset $B$ of $G$ with $| B | > | G | / k^{1 / 3}$ we have $B^{3} = G$ . We use this to obtain improved versions of recent deep theorems of Helfgott and of Shalev concerning product decompositions of finite simple groups, with much simpler proofs. On the other hand, we prove a version of Jordan’s theorem which implies that if $k \geq 2$ , then $G$ has a...