Blocks of full defect with nonabelian metacyclic defect groups

Let p be an odd prime and let B be a p-block of a finite group G with a nonabelian metacyclic defect group P which is a Sylow p-subgroup of G. The purpose of this article is to study the ordinary and modular irreducible characters in B. In particular, we calculate k _i (B) and l _i (B) for an arbitrary nonnegative integer i.     

Locally graded groups with complemented infinite nonabelian subgroups

Infinite nonabelian groups with complemented infinite nonabelian subgroups are investigated. It is proved that, under the condition of being locally graded, these groups are locally finite and solvable, and all nonabelian subgroups are complemented in them if and only if they are non-Chernikov groups.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp, 1098–1100, July–August, 1991.     

Blocks with cyclic defect of Hecke orders of Coxeter groups

Let B\cal B be a p-block of cyclic defect of a Hecke order over the complete ring \Bbb Z[q] _{áq-1,p ?}\Bbb {Z}[q] _{\langle q-1,p \rangle}; i.e. modulo áq-1 ?\langle q-1 \rangle it is a p-block B of cyclic defect of the underlying Coxeter group G. Then B\cal B is a tree order over \Bbb Z[q]_{áq-1, p ?}\Bbb {Z}[q]_{\langle q-1, p \rangle } to the Brauer tree of B. Moreover, in case B\cal B is the principal block of the Hecke order of the symmetric group S(p) on p elements, then B\cal B can be described explicitly. In this case a complete set of non-isomorphic indecomposable Cohen-Macaulay B\cal B-modules is given.     

On groups with relatively small normalizers of nonabelian subgroups

We investigate the structure of a finite nonsolvable group G in which the index |N _G (A): AC _G (A)| is either one or a prime for any nonabelian subgroup A.     

Infinite nonabelian groups with minimal condition for non-normal subgroups

Infinite nonabelian groups which do not possess a descending chain of non-normal subgroups are examined. It is established that under certain additional conditions, in particular the condition of the existence of a normal system with finite factors, the class of all such groups consists only of infinite extremal nonabelian groups and infinite hamiltonian groups, see [6].Translated from Matematicheskie Zametki, Vol. 6, No. 1, pp. 11–18, July, 1969.     

Finite nondispersible groups all subgroups of which with nonprimary index are metacyclic

We describe the structure of finite nondispersible groups all subgroups of which with nonprimary index are metacyclic.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 6, pp. 755–759, June, 1995.     

Blocks with trivial intersection defect groups

We show that each block whose defect groups intersect pairwise trivially either has cyclic or generalised quaternion defect groups, or is Morita equivalent to one of a given list of blocks of central extensions of automorphism groups of non-abelian simple groups. In particular we classify all blocks of automorphism groups of non-abelian simple groups whose defect groups are non-cyclic and intersect pairwise trivially. A consequence is that Donovans conjecture holds for blocks whose defect groups intersect pairwise trivially.in final form: 14 January 2003Mathematics Subject Classification (2000): 20C20This research was supported in part by the Marsden Fund of New Zealand via grant UOA 810.     

Blocks with dihedral defect groups in solvable groups

Mathematische Zeitschrift -     

Solvable infinite-dimensional linear groups with restrictions on the nonabelian subgroups of infinite rank

Under study are the solvable nonabelian linear groups of infinite central dimension and sectional p-rank, p ≥ 0, in which all proper nonabelian subgroups of infinite sectional p-rank have finite central dimension. We describe the structure of the groups of this class.     

Blocks and defect groups of monomial groups

In this paper the p-block structure and the defect groups of finite monomial groups are determined.     

Torsion-free Abelian groups with cyclic p-basic subgroups

We investigate the structure of indecomposable torsion-free Abelian groups all of whose p-basic subgroups are cyclic, and also the structure of the groups and rings of endomorphisms of such groups. We prove the existence of a torsion-free Abelian group of countable rank with cyclic p-basic subgroups which has no indecomposable nonzero direct summands.Translated from Matematicheskie Zametki, Vol. 20, No. 6, pp. 805–813, December, 1976.