arXiv subjects

A. Tortora

Publications and source records attributed to A. Tortora.

6 recordsLinked to original sources

arXiv2015

On varieties of groups satisfying an Engel type identity

Let m, n be positive integers, v a multilinear commutator word and w = v^m. Denote by v(G) and w(G) the verbal subgroups of a group G corresponding to v and w, respectively. We prove that the class of all groups G in which the w-values are n-Engel and w(G) is locally nilpotent is a variety (Theorem A). Further, we show that in the case where m is a prime-power the class of all groups G in which the w-values are n-Engel and v(G) has an ascending normal series whose quotients are either locally soluble or locally finite is a variety (Theorem B). We examine the question whether the latter result remains valid with m allowed to be an arbitrary positive integer. In this direction, we show that if m, n are positive integers, u a multilinear commutator word and v the product of 896 u-words, then the class of all groups G in which the v^m-values are n-Engel and the verbal subgroup u(G) has an ascending normal series whose quotients are either locally soluble or locally finite is a variety (Theorem C).

math.GR↗

arXiv2015

A generalization of 2-Baer groups

A group in which all cyclic subgroups are 2-subnormal is called a 2-Baer group. The topic of this paper are generalized 2-Baer groups, i.e. groups in which the non-2-subnormal cyclic subgroups generate a proper subgroup of the group. If this subgroup is non-trivial, the group is called a generalized T_2-group. In particular, we provide structure results for such groups, investigate their nilpotency class and construct examples of finite p-groups which are generalized T_2-groups.

math.GR↗

arXiv2014

The Engel elements in generalized FC-groups

We generalize to FC*, the class of generalized FC-groups introduced in [F. de Giovanni, A. Russo, G. Vincenzi, Groups with restricted conjugacy classes, Serdica Math. J. 28 (2002), 241-254], a result of Baer on Engel elements. More precisely, we prove that the sets of left Engel elements and bounded left Engel elements of an FC*-group G coincide with the Fitting subgroup; whereas the sets of right Engel elements and bounded right Engel elements of G are subgroups and the former coincides with the hypercentre. We also give an example of an FC*-group for which the set of right Engel elements contains properly the set of bounded right Engel elements.

math.GR↗

arXiv2014

An Engel condition for orderable groups

Let m,n be positive integers, v a multilinear commutator word and w=v^m. We prove that if G is an orderable group in which all w-values are n-Engel, then the verbal subgroup v(G) is locally nilpotent. We also show that in the particular case where v=x the group G is nilpotent (rather than merely locally nilpotent).

math.GR↗

arXiv2010

SAGACE: the Spectroscopic Active Galaxies And Clusters Explorer

The SAGACE experiment consists of a mm/sub-mm telescope with a 3-m diameter primary mirror, coupled to a cryogenic multi-beam differential spectrometer. SAGACE explores the sky in the 100-760 GHz frequency range, using four diffraction-limited bolometer arrays. The instrument is designed to perform spectroscopic surveys of the Sunyaev-Zeldovich effects of thousands of galaxy clusters, of the spectral energy distribution of active galactic nuclei, and of the [CII] line of a thousand galaxies in the redshift desert. In 2008 a full phase-A study for a national small mission was completed and delivered to the Italian Space Agency (ASI). We have shown that taking advantage of the differential operation of the Fourier Transform Spectrometer, this ambitious instrument can operate from a Molniya orbit, and can be built and operated within the tight budget of a small mission.

astro-ph.CO↗

arXiv2003

Monomial invariants in codimension two

We define the monomial invariants of a projective variety $Z$; they are invariants coming from the generic initial ideal of $Z$. Using this notion, we generalize a result of Cook: If $Z$ is an integral variety of codimension two, satisfying the additional hypothesis $s_Z=s_Γ,$ then its monomial invariants are connected.

math.AG↗