On the (2,3)-generation of the finite symplectic groups

This paper is a new important step towards the complete classification of the finite simple groups which are $(2,3)$-generated. In fact, we prove that the symplectic groups $Sp_{2n}(q)$ are $(2,3)$-generated for all $n\geq 4$. Because of the existing literature, this result implies that the groups $PSp_{2n}(q)$ are $(2,3)$-generated for all $n\geq 2$, with the exception of $PSp_4(2^f)$ and $PSp_4(3^f)$

The simple classical groups of dimension less than 6 which are (2,3)-generated

In this paper we determine the classical simple groups of dimension r=3,5 which are (2,3)-generated (the cases r = 2, 4 are known). If r = 3, they are PSL_3(q), q 4, and PSU_3(q^2), q^2 9, 25. If r = 5 they are PSL_5(q), for all q, and PSU_5(q^2), q^2 >= 9. Also, the soluble group PSU_3(4) is not (2,3)-generated. We give explicit (2,3)-generators of the linear preimages, in the special linear groups, of the (2,3)-generated simple groups.Comment: 12 page

The (2,3)(2,3)-generation of the finite unitary groups

In this paper we prove that the unitary groups $SU_n(q^2)$ are $(2,3)$-generated for any prime power $q$ and any integer $n\geq 8$. By previous results this implies that, if $n\geq 3$, the groups $SU_n(q^2)$ and $PSU_n(q^2)$ are $(2,3)$-generated, except when $(n,q)\in\{(3,2),(3,3),(3,5),(4,2), (4,3),(5,2)\}$.Comment: In this version, we obtained a complete classification of the finite simple unitary groups which are (2,3)-generated; some proofs have been semplifie

Scott's formula and Hurwitz groups

This paper continues previous work, based on systematic use of a formula of L. Scott, to detect Hurwitz groups. It closes the problem of determining the finite simple groups contained in $PGL_n(F)$ for $n\leq 7$ which are Hurwitz, where $F$ is an algebraically closed field. For the groups $G_2(q)$, $q\geq 5$, and the Janko groups $J_1$ and $J_2$ it provides explicit $(2,3,7)$-generators

More on regular subgroups of the affine group

This paper is a new contribution to the study of regular subgroups of the affine group $AGL_n(F)$, for any field $F$. In particular we associate to any partition $\lambda\neq (1^{n+1})$ of $n+1$ abelian regular subgroups in such a way that different partitions define non-conjugate subgroups. Moreover, we classify the regular subgroups of certain natural types for $n\leq 4$. Our classification is equivalent to the classification of split local algebras of dimension $n+1$ over $F$. Our methods, based on classical results of linear algebra, are computer free

The (2,3)-generation of the special unitary groups of dimension 6

In this paper we give explicit (2,3)-generators of the unitary groups SU_6(q^ 2), for all q. They fit into a uniform sequence of likely (2,3)-generators for all n>= 6

The (2,3)(2,3)-generation of the finite simple orthogonal groups, I

The complete classification of the finite simple groups that are $(2,3)$-generated is a problem which is still open only for orthogonal groups. Here, we construct $(2, 3)$-generators for the finite odd-dimensional orthogonal groups $\Omega_{2k+1}(q)$ with $q$ odd and $k\geq 4$. As a byproduct we also obtain $(2,3)$-generators for $\Omega_{4k}^+(q)$ with $k\geq 3$ and $q$ odd, and for $\Omega_{4k+2}^\pm(q)$ with $k\geq 4$ and $q\equiv \pm 1 \pmod 4$

Differences in the activity and distribution of peroxidase from three different portions of germinative Brassica oleracea seeds.

Peroxidase (POD, EC 1.11.1.7) activity, cellular localization and isozyme patterns were investigated in the seed integument, cotyledon and embryo axis of Brassica oleracea cv. Cappuccio during pregermination and seedling growth. Seeds started to germinate after 24 h of imbibition. POD activity was localized in the pigmented layer of the integument and in procambial strands of the cotyledon and embryo axis in the first 24 h of imbibition. It was localized in the integumental cells of palisade, pigmented and aleurone layers and in epidermal, meristematic, procambial cells and xylem elements of the root and hypocotyl after 48 h of imbibition. POD activity increased during germination and early seedling growth: in the integument, it reached a maximum value after 72 h of imbibition, in the embryo axis and cotyledons, it increased up to 144 h of imbibition. The increase in peroxidase activity was accompanied by the appearance of new isozymes correlated with the development of seedling tissues. The isozyme profile was characterized by nine peroxidases: isoperoxidase of 50 kDa peculiar to integuments, that of 150 kDa to cotyledons and that of 82 kDa to the embryo axis. During pregerminative phase isozymes of 84 kDa were detected in the integument and cotyledons, of 48.5 kDa in the embryo axis. After germination, peroxidase activity and the complexity of the isozyme pattern increased, suggesting that they play a relevant role after rupture of the integument

Circularly Polarized Resonant Rayleigh Scattering and Skyrmions in the ν\nu = 1 Quantum Hall Ferromagnet

We use the circularly polarized resonant Rayleigh scattering (RRS) to study the quantum Hall ferromagnet at $\nu$ = 1. At this filling factor we observe a right handed copolarized RRS which probes the Skyrmion spin texture of the electrons in the photoexcited grounds state. The resonant scattering is not present in the left handed copolarization, and this can be related to the correlation between Skymionic effects, screening and spin wave excitations. These results evidence that RRS is a valid method for the study of the spin texture of the quantum Hall states