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Periodic linear groups factorized by mutually permutable subgroups

Maria Ferrara, Marco Trombetti (2023)

Czechoslovak Mathematical Journal

The aim is to investigate the behaviour of (homomorphic images of) periodic linear groups which are factorized by mutually permutable subgroups. Mutually permutable subgroups have been extensively investigated in the finite case by several authors, among which, for our purposes, we only cite J. C. Beidleman and H. Heineken (2005). In a previous paper of ours (see M. Ferrara, M. Trombetti (2022)) we have been able to generalize the first main result of J. C. Beidleman, H. Heineken (2005) to periodic...

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

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.

P-localization of some classes of groups.

Augusto Reynol Filho (1993)

Publicacions Matemàtiques

The aim for the present paper is to study the theory of P-localization of a group in a category C such that it contains the category of the nilpotent groups as a full sub-category. In the second section we present a number of results on P-localization of a group G, which is the semi-direct product of an abelian group A with a group X, in the category G of all groups. It turns out that the P-localized (GP) is completely described by the P-localized XP of X, A and the action w of X on A. In the third...

P-nilpotent completion is not idempotent.

Geok Choo Tan (1997)

Publicacions Matemàtiques

Let P be an arbitrary set of primes. The P-nilpotent completion of a group G is defined by the group homomorphism η: G → GP' where GP' = inv lim(G/ΓiG)P. Here Γ2G is the commutator subgroup [G,G] and ΓiG the subgroup [G, Γi−1G] when i > 2. In this paper, we prove that P-nilpotent completion of an infinitely generated free group F does not induce an isomorphism on the first homology group with ZP coefficients. Hence, P-nilpotent completion is not idempotent. Another important consequence of...

Polynomial invariants of 2-component links.

Kunio Murasugi (1985)

Revista Matemática Iberoamericana

Let L = X U Y be an oriented 2-component link in S3. In this paper we will define two different types of polynomials which are ambient isotopic invariants of L. One is associated with a cyclic cover branched along one of their components, an the other is associated with a metabelian cover of L. This invariants are defined for any link unless the linking number lk(X,Y), is ±1.

Polynomials over Q solving an embedding problem

Nuria Vila (1985)

Annales de l'institut Fourier

The fields defined by the polynomials constructed in E. Nart and the author in J. Number Theory 16, (1983), 6–13, Th. 2.1, with absolute Galois group the alternating group A n , can be embedded in any central extension of A n if and only if n ≡ 0 ( m o d 8 ) , or n ≡ 2 ( m o d 8 ) and n is a sum of two squares. Consequently, for theses values of n , every central extension of A n occurs as a Galois group over Q .

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