Results 61 to 70 of about 53,696 (220)
Extensions of Johnson's and Morita's homomorphisms that map to finitely generated abelian groups
, 2009 We extend each higher Johnson homomorphism to a crossed homomorphism from the automorphism group of a finite-rank free group to a finite-rank abelian group. We also extend each Morita homomorphism to a crossed homomorphism from the mapping class group of
Corwin L. J. +2 more
core +1 more source
Locally Nilpotent Linear Groups [PDF]
Irish Mathematical Society Bulletin, 2005 We survey aspects of locally nilpotent linear groups. Then we obtain a new classification; namely, we classify the irreducible maximal locally nilpotent subgroups of $\mathrm{GL}(q, \mathbb F)$ for prime $q$ and any field $\mathbb F$.
A. S. Detinko +2 more
openaire +2 more sources
Spectra of subrings of cohomology generated by characteristic classes for fusion systems
Bulletin of the London Mathematical Society, EarlyView.Abstract If F$\mathcal {F}$ is a saturated fusion system on a finite p$p$‐group S$S$, we define the Chern subring Ch(F)${\operatorname{Ch}}(\mathcal {F})$ of F$\mathcal {F}$ to be the subring of H∗(S;Fp)$H^*(S;{\mathbb {F}}_p)$ generated by Chern classes of F$\mathcal {F}$‐stable representations of S$S$. We show that Ch(F)${\operatorname{Ch}}(\mathcal {
Ian J. Leary, Jason Semeraro
wiley +1 more source
Coloured shuffle compatibility, Hadamard products, and ask zeta functions
Bulletin of the London Mathematical Society, EarlyView.Abstract We devise an explicit method for computing combinatorial formulae for Hadamard products of certain rational generating functions. The latter arise naturally when studying so‐called ask zeta functions of direct sums of modules of matrices or class‐ and orbit‐counting zeta functions of direct products of nilpotent groups.
Angela Carnevale +2 more
wiley +1 more source
Partially S-embedded minimal subgroups of finite groups [PDF]
International Journal of Group Theory, 2013 Suppose that H is a subgroup of G, then H is said to be s-permutable in G, if H permutes with every Sylow subgroup of G. If HP=PH hold for every Sylow subgroup P of G with (|P|, |H|)=1), then H is called an s-semipermutable subgroup of G.
Tao Zhao, Qingliang Zhang
doaj
Automorphisms fixing every normal subgroup of a nilpotent-by-abelian group
, 2007 Among other things, we prove that the group of automorphisms fixing every normal subgroup of a nilpotent-by-abelian group is nilpotent-by-metabelian. In particular, the group of automorphisms fixing every normal subgroup of a metabelian group is soluble ...
Endimioni, G.
core +1 more source
Random Nilpotent Groups I [PDF]
International Mathematics Research Notices, 2017 We study random nilpotent groups in the well-established style of random groups, by choosing relators uniformly among freely reduced words of (nearly) equal length and letting the length tend to infinity. Whereas random groups are quotients of a free group by such a random set of relators, random nilpotent groups are formed as corresponding quotients ...
Andrew P. Sánchez +4 more
openaire +3 more sources
On the universal pairing for 2‐complexes
Bulletin of the London Mathematical Society, EarlyView.Abstract The universal pairing for manifolds was defined and shown to lack positivity in dimension 4 in [Freedman, Kitaev, Nayak, Slingerland, Walker, and Wang, J. Geom. Topol. 9 (2005), 2303–2317]. We prove an analogous result for 2‐complexes, and show that the universal pairing does not detect the difference between simple homotopy equivalence and 3 ...
Mikhail Khovanov +2 more
wiley +1 more source
On free subgroups of finite exponent in circle groups of free nilpotent algebras [PDF]
International Journal of Group Theory, 2019 Let $K$ be a commutative ring with identity and $N$ the free nilpotent $K$-algebra on a non-empty set $X$. Then $N$ is a group with respect to the circle composition. We prove that the subgroup generated by $X$ is relatively free in a suitable class
Juliane Hansmann
doaj +1 more source
Nilpotent groups and their generalizations [PDF]
Transactions of the American Mathematical Society, 1940 Nilpotent finite groups may be defined by a great number of properties. Of these the following three may be mentioned, since they will play an important part in this investigation. (1) The group is swept out by its ascending central chain (equals its hypercentral). (2) The group is a direct product of p-groups (that is, of its primary components).
openaire +2 more sources