46 research outputs found
A non-LEA Sofic Group
We describe elementary examples of finitely presented sofic groups which are
not residually amenable (and thus not initially subamenable or LEA, for short).
We ask if an amalgam of two amenable groups over a finite subgroup is
residually amenable and answer this positively for some special cases,
including countable locally finite groups, residually nilpotent groups and
others.Comment: The main theorem is strengthened so that the Sofic examples are shown
to have no co-amenable LEA subgroup
Asymptotically CAT(0) groups
We develop a general theory for asymptotically CAT(0) groups; these are groups acting geometrically on a geodesic space, all of whose asymptotic cones are CAT(0)
One Relator Quotients of Graph Products
In this paper, we generalise Magnus' Freiheitssatz and solution to the word
problem for one-relator groups by considering one relator quotients of certain
classes of right-angled Artin groups and graph products of locally indicable
polycyclic groups
2D problems in groups
We investigate a conjecture about stabilisation of deficiency in finite index
subgroups and relate it to the D2 Problem of C.T.C. Wall and the Relation Gap
problem. We verify the pro- version of the conjecture, as well as its higher
dimensional abstract analogues.Comment: comments welcome, some references added in v
Ping pong on CAT(0) cube complexes
Let be a group acting properly and essentially on an irreducible,
non-Euclidean finite dimensional CAT(0) cube complex without fixed points
at infinity. We show that for any finite collection of simultaneously
inessential subgroups in , there exists an element
of infinite order such that , . We apply this to show that any group, acting faithfully and
geometrically on a non-Euclidean possibly reducible CAT(0) cube complex, has
property i.e. given any finite list of
elements from , there exists of infinite order such that ,
. This
applies in particular to the Burger-Moses simple groups that arise as lattices
in products of trees. The arguments utilize the action of the group on its
Poisson boundary and moreover, allow us to summarise equivalent conditions for
the reduced -algebra of the group to be simple
Asymptotically CAT(0) groups
We develop a general theory for asymptotically CAT(0) groups; these are groups acting geometrically on a geodesic space, all of whose asymptotic cones are CAT(0)
On Property (FA) for wreath products
We characterize permutational wreath products with Property (FA). For
instance, the standard wreath product A wr B of two nontrivial countable groups
A,B, has Property (FA) if and only if B has Property (FA) and A is a finitely
generated group with finite abelianisation. We also prove an analogous result
for hereditary Property (FA). On the other hand, we prove that many wreath
products with hereditary Property (FA) are not quotients of finitely presented
groups with the same property.Comment: 12 pages, 0 figur
Rayleigh quotients of Dillon's functions
The Walsh--Hadamard spectrum of a bent function uniquely determines a dual
function. The dual of a bent function is also bent. A bent function that is
equal to its dual is called a self-dual function. The Hamming distance between
a bent function and its dual is related to its Rayleigh quotient. Carlet,
Danielsen, Parker, and Sole studied Rayleigh quotients of bent functions in
, and obtained an expression in terms of a character sum.
We use another approach comprising of Desarguesian spreads to obtain the
complete spectrum of Rayleigh quotients of bent functions in