3,579 research outputs found
Subgroups of direct products of two limit groups
If S is a subgroup of a direct product of two limit groups, and S is of type
FP(2) over the rationals, then S has a subgroup of finite index that is a
direct product of at most two limit groups.Comment: 18 pages, no figure
Normalisers in Limit Groups
Let \G be a limit group, S\subset\G a subgroup, and the normaliser of
. If has finite \Q-dimension, then is finitely
generated and either is finite or is abelian. This result has
applications to the study of subdirect products of limit groups.Comment: 10 pages, no figure
Subgroups of direct products of elementarily free groups
We exploit Zlil Sela's description of the structure of groups having the same
elementary theory as free groups: they and their finitely generated subgroups
form a prescribed subclass E of the hyperbolic limit groups.
We prove that if are in E then a subgroup is of type \FP_n if and only if is itself,
up to finite index, the direct product of at most groups from .
This answers a question of Sela.Comment: 19 pages, no figure
Finite complete rewriting systems for regular semigroups
It is proved that, given a (von Neumann) regular semigroup with finitely many
left and right ideals, if every maximal subgroup is presentable by a finite
complete rewriting system, then so is the semigroup. To achieve this, the
following two results are proved: the property of being defined by a finite
complete rewriting system is preserved when taking an ideal extension by a
semigroup defined by a finite complete rewriting system; a completely 0-simple
semigroup with finitely many left and right ideals admits a presentation by a
finite complete rewriting system provided all of its maximal subgroups do.Comment: 11 page
(1RS,2SR,7RS,8RS)-N-Benzoyltricyclo[6.2.2.0²,⁷]dodeca-9,11-diene-1,10-dicarboximide
The title 1,4-photoadduct, C₂₁H₁₉NO₃, was formed on irradiation of N-benzoylphthalimide in dichloromethane containing cyclohexene. The bond lengths and angles are generally within the normal ranges. A notable feature of the molecule is the presence within it of four contiguous chiral centres
4',5',6',7'-Tetrachlorospiro[cyclohex-2-ene-1,2'-indan]-1',3'-dione
The title compound, C₁₄H₈Cl₄O₂, has been isolated following irradiation of a dichloromethane solution of N-acetyltetrachlorophthalimide and cyclohexene. The structure refinement is slightly compromised by the disorder over two positions of equal occupancy of a methylene groupβ to the spiro C atom
Subgroups of direct products of limit groups
If are limit groups and is of
type \FP_n(\mathbb Q) then contains a subgroup of finite index that is
itself a direct product of at most limit groups. This settles a question of
Sela.Comment: 20 pages, no figures. Final version. Accepted by the Annals of
Mathematic
Benzylammonium 2,4-bis(dicyanomethylene)-2,3-dihydroisoindolide
The cation and anion of the title salt, C⁷H₁₀N⁺.C₁₄H₄N₅-, are both bisected by a crystallographic mirror plane. Extensive hydrogen bonding, with the R₆⁶(28) graph-set motif, connects the ions into layers
On the finite presentation of subdirect products and the nature of residually free groups
We establish {\em{virtual surjection to pairs}} (VSP) as a general criterion
for the finite presentability of subdirect products of groups: if
are finitely presented and
projects to a subgroup of finite index in
each , then is finitely presentable, indeed there
is an algorithm that will construct a finite presentation for .
We use the VSP criterion to characterise the finitely presented residually
free groups. We prove that the class of such groups is recursively enumerable.
We describe an algorithm that, given a finite presentation of a residually free
group, constructs a canonical embedding into a direct product of finitely many
limit groups. We solve the (multiple) conjugacy problem and membership problem
for finitely presentable subgroups of residually free groups. We also prove
that there is an algorithm that, given a finite generating set for such a
subgroup, will construct a finite presentation.
New families of subdirect products of free groups are constructed, including
the first examples of finitely presented subgroups that are neither
nor of Stallings-Bieri typeComment: 44 pages. To appear in American Journal of Mathematics. This is a
substantial rewrite of our previous Arxiv article 0809.3704, taking into
account subsequent developments, advice of colleagues and referee's comment
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