Lattice subgroups of free congruence groups

Congruence Subgroups of Groups Commensurable with PSL

One-Cusped Congruence Subgroups of Bianchi Groups

We show that there are only finitely many maximal congruence subgroups of the Bianchi groups such that the quotient by H has only one cusp.

Convex $L$-lattice subgroups in $L$-ordered groups

In this paper, we have focused to study convex $L$-subgroups of an $L$-ordered group. First, we introduce the concept of a convex $L$-subgroup and a convex $L$-lattice subgroup of an $L$-ordered group and give some examples. Then we find some properties and use them to construct convex $L$-subgroup generated by a subset $S$ of an $L$-ordered group $G$ . Also, we generalize a well known result a...

Subgroups of Free Metabelian Groups

In 1954 A. G. Howson proved that the intersection of two finitely generated subgroups of a free group is again finitely generated. Now the free metabelian subgroups of a free metabelian group of finite rank n are quite restricted. Indeed they are again of finite rank at most n. This suggests that there may be an analog of Howson’s theorem for free metabelian groups. This turns out not to be the...

Deficiencies of Lattice Subgroups of Lie Groups

Let Γ be a lattice in a connected Lie group. We show that besides a few exceptional cases, the deficiency of Γ is nonpositive.