scholarly journals Weak commutativity and finiteness properties of groups

2018 ◽  
Vol 51 (1) ◽  
pp. 168-180 ◽  
Author(s):  
Martin R. Bridson ◽  
Dessislava H. Kochloukova
Keyword(s):  
Finiteness Properties ◽  
Weak Commutativity

Generalized Commutativity of Lattice-Ordered Groups

2015 ◽  
Vol 65 (2) ◽  
Author(s):  
M. R. Darnel ◽  
W. C. Holland ◽  
H. Pajoohesh
Keyword(s):  
Theorem Proving ◽  
Natural Generalization ◽  
Ordered Groups ◽  
Lattice Ordered Groups ◽  
Weak Commutativity

AbstractIn this paper we explore generalizations of Neumann’s theorem proving that weak commutativity in ordered groups actually implies the group is abelian. We show that a natural generalization of Neumann’s weak commutativity holds for certain Scrimger ℓ-groups.

Finiteness properties of groups

1948 ◽  
Vol 15 (4) ◽  
pp. 1021-1032 ◽  
Author(s):  
Reinhold Baer
Keyword(s):  
Finiteness Properties

scholarly journals Homological finiteness properties of fibre products

2018 ◽  
Vol 69 (3) ◽  
pp. 835-854 ◽  
Author(s):  
Dessislava H Kochloukova ◽  
Francismar Ferreira Lima
Keyword(s):  
Fibre Products ◽  
Finiteness Properties

scholarly journals Stability in the high-dimensional cohomology of congruence subgroups

2020 ◽  
Vol 156 (4) ◽  
pp. 822-861
Author(s):  
Jeremy Miller ◽  
Rohit Nagpal ◽  
Peter Patzt
Keyword(s):  
Congruence Subgroup ◽  
Stability Result ◽  
High Dimensional ◽  
Vanishing Theorem ◽  
Congruence Subgroups ◽  
Codimension One ◽  
Representation Stability ◽  
Steinberg Module ◽  
Finiteness Properties ◽  
Special Case

We prove a representation stability result for the codimension-one cohomology of the level-three congruence subgroup of $\mathbf{SL}_{n}(\mathbb{Z})$. This is a special case of a question of Church, Farb, and Putman which we make more precise. Our methods involve proving finiteness properties of the Steinberg module for the group $\mathbf{SL}_{n}(K)$ for $K$ a field. This also lets us give a new proof of Ash, Putman, and Sam’s homological vanishing theorem for the Steinberg module. We also prove an integral refinement of Church and Putman’s homological vanishing theorem for the Steinberg module for the group $\mathbf{SL}_{n}(\mathbb{Z})$.

Sign in / Sign up

Export Citation Format

Share Document