Suppose that a group G acts transitively on the points of P, a finite non-Desarguesian projective plane. We prove first that the Sylow 2subgroups of G are cyclic or generalized quaternion; we then prove that if G is insoluble then G/O(G) is isomorphic to SL2(5) or SL2(5).2. MSC(2000): 20B25, 51A35.

A subgroup H is said to be nc-supplemented in a group G if there is a subgroup K ≤ G such that HK G and H ∩ K is contained in HG, the core of H in G. We characterize the solvability of finite groups G with some subgroups of Sylow subgroups nc-supplemented in G. We also give a result on c-supplemented subgroups.

Let S be a 2-group. The rank (normal rank) of S is the maximal dimension of an elementary abelian subgroup (a normal elementary abelian subgroup) of S over Z2. The purpose of this article is to determine the rank and normal rank of S, where S is a Sylow 2-subgroup of the classical groups of odd characteristic.

We classify the permutation groups of cyclic codes over a finite field. As a special case, we find the permutation groups of non-primitive BCH codes of prime length. In addition, the Sylow p-subgroup of the permutation group is given for many cyclic codes of length p. Several examples are given to illustrate the results.

is called the 2-class field tower of k. If n is the minimal integer such that kn = kn+1, then n is called the length of the tower. If no such n exists, then the tower is said to be of infinite length. At present there is no known decision procedure to determine whether or not the (2-)class field tower of a given field k is infinite. However, it is known by group theoretic results (see [2]) that...

In this paper, without using the classification of finite simple groups, we determine the structure of  finite simple groups whose Sylow 3-subgroups are of the order 9. More precisely, we classify finite simple groups whose Sylow 3-subgroups are elementary abelian of order 9.

Let p be any prime. P n a Sylow -subgroup of the symmetric group S . ϕ and ψ linear characters let N normaliser in In this article we show that inductions to are equal if, only –conjugate. This is an analogue for groups result Navarro -solvable groups.

A conjecture of Michel Brou e states that if D is an abelian Sylow p-subgroup of a nite group G, and H = N G (D), then the principal blocks of G and H are Rickard equivalent. The structure of groups with abelian Sylow p-subgroups, as determined by P. Fong and M.E. Harris, raises the following question: assuming that Brou e's conjecture holds for the simple components of G, under what conditions...

In this paper, we define a generalized Wielandt subgroup, local generalized Wielandt subgroup and its series for finite group and discuss its different basic properties which explain the notion of generalized Wielandt subgroup in a better way. We bound generalized Wielandt length as a function of nilpotency classes of its Sylow subgroups.

There is a longstanding conjecture, due to Gregory Cherlin and Boris Zilber, that all simple groups of finite Morley rank are simple algebraic groups. Towards this end, the development of the theory of groups of finite Morley rank has achieved a good theory of Sylow 2-subgroups. It is now common practice to divide the Cherlin-Zilber conjecture into different cases depending on the nature of the...