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A geometric approach to on-diagonal heat kernel lower bounds on groups

Thierry Coulhon, Alexander Grigor'yan, Christophe Pittet (2001)

Annales de l’institut Fourier

We introduce a new method for obtaining heat kernel on-diagonal lower bounds on non- compact Lie groups and on infinite discrete groups. By using this method, we are able to recover the previously known results for unimodular amenable Lie groups as well as for certain classes of discrete groups including the polycyclic groups, and to give them a geometric interpretation. We also obtain new results for some discrete groups which admit the structure of a semi-direct product or of a wreath product....

Abelian quasinormal subgroups of groups

Stewart E. Stonehewer, Giovanni Zacher (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let G be any group and let A be an abelian quasinormal subgroup of G . If n is any positive integer, either odd or divisible by 4 , then we prove that the subgroup A n is also quasinormal in G .

An elementary class extending abelian-by- G groups, for G infinite

Carlo Toffalori (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We show that for no infinite group G the class of abelian-by- G groups is elementary, but, at least when G is an infinite elementary abelian p -group (with p prime), the class of groups admitting a normal abelian subgroup whose quotient group is elementarily equivalent to G is elementary.

Asphericity of symmetric presentations

Fulvia Spaggiari (2006)

Publicacions Matemàtiques

Using the notion of relative presentation due to Bogley and Pride, we give a new proof of a theorem of Prishchepov on the asphericity of certain symmetric presentations of groups. Then we obtain further results and applications to topology of low-dimensional manifolds.

Bicyclic commutator quotients with one non-elementary component

Daniel Mayer (2023)

Mathematica Bohemica

For any number field K with non-elementary 3 -class group Cl 3 ( K ) ≃ C 3 e × C 3 , e ≥ 2 , the punctured capitulation type ϰ ( K ) of K in its unramified cyclic cubic extensions L i , 1 ≤ i ≤ 4 , is an orbit under the action of S 3 × S 3 . By means of Artin’s reciprocity law, the arithmetical invariant ϰ ( K ) is translated to the punctured transfer kernel type ϰ ( G 2 ) of the automorphism group G 2 = Gal ( F 3 2 ( K ) / K ) of the second Hilbert 3 -class field of K . A classification of finite 3 -groups G with low order and bicyclic commutator quotient G / G ' ≃ C 3 e × C 3 , 2 ≤ e ≤ 6 , according to the algebraic invariant...

Calculating the genus of a direct product of certain nilpotent groups.

Peter Hilton, Dirk Scevenels (1995)

Publicacions Matemàtiques

The Mislin genus G(N) of a finitely generated nilpotent group N with finite commutator subgroup admits an abelian group structure. If N satisfies some additional conditions -we say that N belongs to N1- we know exactly the structure of G(N). Considering a direct product N1 x ... x Nk of groups in N1 takes us virtually always out of N1. We here calculate the Mislin genus of such a direct product.

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