7,804 research outputs found
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 -generated. In fact, we prove that the
symplectic groups are -generated for all . Because
of the existing literature, this result implies that the groups
are -generated for all , with the exception of and
More on regular subgroups of the affine group
This paper is a new contribution to the study of regular subgroups of the
affine group , for any field . In particular we associate to any
partition of 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 . Our
classification is equivalent to the classification of split local algebras of
dimension over . Our methods, based on classical results of linear
algebra, are computer free
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
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 for which are Hurwitz,
where is an algebraically closed field. For the groups , ,
and the Janko groups and it provides explicit -generators
The -generation of the finite unitary groups
In this paper we prove that the unitary groups are
-generated for any prime power and any integer . By
previous results this implies that, if , the groups and
are -generated, except when
.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
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
On characters of Chevalley groups vanishing at the non-semisimple elements
Let G be a finite simple group of Lie type. In this paper we study characters
of G that vanish at the non-semisimple elements and whose degree is equal to
the order of a maximal unipotent subgroup of G. Such characters can be viewed
as a natural generalization of the Steinberg character. For groups G of small
rank we also determine the characters of this degree vanishing only at the
non-identity unipotent elements.Comment: Dedicated to Lino Di Martino on the occasion of his 65th birthda
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