Sylow subgroups of finitary linear groups

In this paper we describe the structure and the conjugacy classes of Sylow p-subgroups of FGL(V, ), the group of finitary -automorphisms of the -vector space V.The Author is member of the GNSAGA.     

Large orbits of elements centralized by a Sylow subgroup

If G has a nilpotent normal p-complement and V is a finite, faithful and completely reducible G-module of characteristic p, we prove that there exist ${v_1, v_2 \in V}If G has a nilpotent normal p-complement and V is a finite, faithful and completely reducible G-module of characteristic p, we prove that there exist v₁, v₂ ? V{v_1, v_2 \in V} such that C_G(v₁)?C_G(v₂) = P{{\bf C}_{G}{(v_1)}\cap {\bf C}_{G}{(v_2)} = P} , where P ? Syl_p(G){P \in {\rm Syl}_p(G)} . We hence deduce that, if the normal p-complement K is nontrivial, there exists v ? C_V(P){v \in {\bf C}_{V}(P)} such that |K : C _K (v)|² > |K|.     

Finite non-solvable groups in which the normalizer of every nonnormal cyclic subgroup is maximal

It is well known that the normality of subgroups plays an important part in the research of group theory. So it is reasonable to investigate the structure of a group by using normalizers of some kind of subgroups. In this paper we mainly investigate the structure of non-solvable groups in which the normalizer of every non-normal cyclic subgroup is a maximal subgroup, and finally the classification for this kind of groups is given.     

On collineation groups of a projective plane of prime order

Towards the study of finite projective plane of prime order, the following result is proved in this paper. Let be a projective plane of prime order p and let G be a collineation group of . If p¦|G|, then either is Desarguesian or the maximal maximal normal subgroup of G is not trivial. In particular, is Desarguesian if G does not leave invariant any point or line.Partially supported by NSERC A8460.Partially supported by CNPq.     

Symmetric and general linear groups with supersoluble Sylow normalizers

Sunto Nel presente lavoro vengono caratterizzati i gruppi finiti che hanno i normalizzanti dei sottogruppi di Sylow supersolubili e che appartengono alle seguenti classi: gruppi simmetrici, alterni, lineari generali e lineari speciali.     

Collineation groups preserving a unital in a projective plane of even order

We investigate the structure of a collineation group G leaving invariant a unital U in a finite projective plane of even order n=m ². When G is transitive on the points of U and the socle of G has even order, then must be a Desarguesian plane, U a classical unital and PSU(3,m ²)GPU(3,m ²) — for m>2. The primitive case follows as an easy corollary.This research was supported by a grant from the M.P.I.     

On finitary linear groups with a locally nilpotent maximal subgroup

We prove that a group G of finitary permutations, containing a locally nilpotent maximal subgroup M is locally solvable if M is not a 2-group. We also prove that the same is true if G is a periodic, non-modular, finitary linear group.     

Central Schur rings over the projective special linear groups

In [1 Bannai, E. (1991). Subschemes of some association schemes. J. Algebra 14:167–188.[Crossref], [Web of Science ®] , [Google Scholar]], Bannai presents a fusion condition and uses this to consider central Schur rings (S-rings) over the simple groups PSL(2,q) where q is a prime power. In this paper, we concretely describe all such S-rings in terms of symmetric S-rings over cyclic groups. The final section discusses counting these.