R-groups and parameters

More R-sequenceable Groups

Behavior of $R$-groups for $p$-adic inner forms of quasi-split special unitary groups

‎We study $R$-groups for $p$-adic inner forms of quasi-split special unitary groups‎. ‎We prove Arthur's conjecture‎, ‎the isomorphism between the Knapp-Stein $R$-group and the Langlands-Arthur $R$-group‎, ‎for quasi-split special unitary groups and their inner forms‎. ‎Furthermore‎, ‎we investigate the invariance of the Knapp-Stein $R$-group within $L$-packets and between inner forms‎. ‎This w...

R-sequenceability and R*-sequenceability of abelian 2-groups

A group of order n is said to be R-sequenceable if the nonidentity elements of the group can be listed in a sequence a,, a,, . . . , a,_ 1 such that the quotients a; ‘az, a; ’ a3, . , a;?,a,_ r, a.-_‘,a, are distinct. An abelian group is R*-sequenceable if it has an R-sequencing a,, a,, . . , a,, _ 1 such that a,_ ra, + r = ai for some i (subscripts are read modulo n 1). Friedlander, Gordon and...

Limit groups and groups acting freely on R n-trees.

We give a simple proof of the finite presentation of Sela's limit groups by using free actions on R n-trees. We first prove that Sela's limit groups do have a free action on an R n-tree. We then prove that a finitely generated group having a free action on an R n-tree can be obtained from free abelian groups and surface groups by a finite sequence of free products and amalgamations over cyclic ...

Limit groups and groups acting freely on R–trees

We give a simple proof of the finite presentation of Sela’s limit groups by using free actions on Rn–trees. We first prove that Sela’s limit groups do have a free action on an Rn–tree. We then prove that a finitely generated group having a free action on an Rn–tree can be obtained from free abelian groups and surface groups by a finite sequence of free products and amalgamations over cyclic gro...