Maximal Divisible Subgroups in Modular Group Rings

Basic Subgroups in Commutative Modular Group Rings

Let S(RG) be a normed Sylow p-subgroup in a group ring RG of an abelian group G with p-component Gp and a p-basic subgroup B over a commutative unitary ring R with prime characteristic p. The first central result is that 1 + I(RG;Bp) + I(R(p)G;G) is basic in S(RG) and B[1 + I(RG;Bp) + I(R(p )G;G)] is p-basic in V (RG), and [1 + I(RG;Bp) + I(R(p )G;G)]Gp/Gp is basic in S(RG)/Gp and [1 + I(RG;Bp)...

Maximal Nonparabolic Subgroups of the Modular Group

The elliptic elements of M, each with two conjugate complex fixed points, are precisely the conjugates of nontrivial powers of A and B. The parabolic elements, each with a single real fixed point, are precisely the conjugates of nontrivial powers of C = AB: z ~ z + 1. The remaining nontrivial elements of M are hyperbolic, each with two real fixed points. A subgroup S of M is torsionfree (and th...

On the Balanced Subgroups of Modular Group Rings

Let S(RG) be the normed p-unit group in a group ring RG, formed by an abelian group G and a commutative ring R with identity of prime characteristic p. All unexplained symbols and letters as well as the terminology and definitions from the abelian group theory (including the topological ones) can be found in the classical book monographs [7]. For a background material in that direction, we refe...

Characterizing the Multiplicative Group of a Real Closed Field in Terms of its Divisible Maximal Subgroup

Endomorphism Rings of Permutation Modules over Maximal Young Subgroups

Let K be a field of characteristic two, and let λ be a two-part partition of some natural number r. Denote the permutation module corresponding to the (maximal) Young subgroup Σλ in Σr byM . We construct a full set of orthogonal primitive idempotents of the centraliser subalgebra SK(λ) = 1λSK(2, r)1λ = EndKΣr (M ) of the Schur algebra SK(2, r). These idempotents are naturally in one-to-one corr...