3,530 research outputs found
On w-maximal groups
Let be a word, i.e. an element of the free group on generators . The verbal subgroup of
a group is the subgroup generated by the set of all -values in . We say that a (finite)
group is -maximal if for all proper subgroups
of and that is hereditarily -maximal if every subgroup of is
-maximal. In this text we study -maximal and hereditarily -maximal
(finite) groups.Comment: 15 page
On P-saturable groups
AbstractA pro-p group G is a PF-group if it has central series of closed subgroups {Ni}i∈N with trivial intersection satisfying N1=G and [Ni,G,…p−1,G]⩽Ni+1p. In this paper, we prove that a finitely generated pro-p group G is a p-saturable group, in the sense of Lazard, if and only if it is a torsion free PF-group. Using this characterization, we study certain families of subgroups of p-saturable groups. For example, we prove that any normal subgroup of a p-saturable group contained in the Frattini is again p-saturable
Algorithms for Del Pezzo Surfaces of Degree 5 (Construction, Parametrization)
It is well known that every Del Pezzo surface of degree 5 defined over k is
parametrizable over k. In this paper we give an efficient construction for
parametrizing, as well as algorithms for constructing examples in every
isomorphism class and for deciding equivalence.Comment: 15 page
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