We determine the torsion subgroup of the group of endotrivial modules for a finite solvable group in characteristic p. We also prove that our result would hold for p-solvable groups, provided a conjecture can be proved about the case of p-nilpotent groups.

The analogue of Lagrangians for symplectic forms over finite groups is studied, motivated by the fact that symplectic G-forms with a normal Lagrangian N⊳G are in one-to-one correspondence, up to inflation, with bijective 1-cocycle data on the quotients G/N . This yields a method to construct groups of central type from such quotients, known as Involutive Yang-Baxter groups. Another motivation f...

We prove that a finite group with nilpotent subgroup H and H-connected transversals is solvable. The proof depends on the classification of finite simple groups.

We prove that every finitely generated nilpotent group of class c admits a polynomial isoperimetric function of degree c+1 and a linear upper bound on its filling length function. 1991 Mathematics Subject Classification: 20F05, 20F32, 57M07

We give methods for bounding the higher-order filling functions of a homogeneous nilpotent group and apply them to a family of quadratically presented groups constructed by S. Chen[9]. We find sharp bounds on some higher-order filling invariants of these groups. In particular, we show that groups with arbitrarily large nilpotency class can have euclidean n-dimensional filling volume and give an...

Let H be a subgroup of a group G. H is said to be S-embedded in G if G has a normal T such that HT is an S-permutable subgroup of G and H ∩ T ≤ H sG, where H denotes the subgroup generated by all those subgroups of H which are S-permutable in G. In this paper, we investigate the influence of minimal S-embedded subgroups on the structure of finite groups. We determine the structure the finite grou...

We give a new proof to the criterion for the normal verbal embeddability of groups. The new construction allows us to consider the normal verbal embeddings of soluble groups, of nilpotent groups, and of SN∗-groups into groups of the same type. We also generalize a theorem of Burnside on embeddings of p-groups into commutator subgroups. MSC 2000: 20E07, 20E10

There are some new developments on Plancherel formula and growth of matrix coefficients for unitary representations of nilpotent Lie groups. These have several consequences for the geometry of weakly symmetric spaces and analysis on parabolic subgroups of real semisimple Lie groups, and to (infinite dimensional) locally nilpotent Lie groups. Many of these consequences are still under developmen...