141 research outputs found
Finite groups have more conjugacy classes
We prove that for every there exists a so that
every group of order has at least conjugacy classes. This sharpens earlier results of
Pyber and Keller. Bertram speculates whether it is true that every finite group
of order has more than conjugacy classes. We answer Bertram's
question in the affirmative for groups with a trivial solvable radical
The variety generated by order algebras
Every ordered set can be considered as an algebra in a natural way. We investigate the variety generated by order algebras. We prove, among other things, that this variety is not finitely based and, although locally finite, it is not contained in any finitely generated variety; we describe the bottom of the lattice of its subvarieties
On a conjecture of Gluck
Let and respectively denote the Fitting subgroup and the
largest degree of an irreducible complex character of a finite group . A
well-known conjecture of D. Gluck claims that if is solvable then
. We confirm this conjecture in the case where
is coprime to 6. We also extend the problem to arbitrary finite groups and
prove several results showing that the largest irreducible character degree of
a finite group strongly controls the group structure.Comment: 16 page
A note on the probability of generating alternating or symmetric groups
We improve on recent estimates for the probability of generating the
alternating and symmetric groups and . In
particular we find the sharp lower bound, if the probability is given by a
quadratic in . This leads to improved bounds on the largest number
such that a direct product of copies
of can be generated by two elements
On the reduction of the CSP dichotomy conjecture to digraphs
It is well known that the constraint satisfaction problem over general
relational structures can be reduced in polynomial time to digraphs. We present
a simple variant of such a reduction and use it to show that the algebraic
dichotomy conjecture is equivalent to its restriction to digraphs and that the
polynomial reduction can be made in logspace. We also show that our reduction
preserves the bounded width property, i.e., solvability by local consistency
methods. We discuss further algorithmic properties that are preserved and
related open problems.Comment: 34 pages. Article is to appear in CP2013. This version includes two
appendices with proofs of claims omitted from the main articl
Modeling and Simulating a Novel Biohydrogen Production Technology as an Integrated Part of a Municipal Wastewater Treatment Plant
A series of mathematical models and simulations was developed and performed using BioWin software suit in order to determine the suitability of implementing a biohydrogen production technology in an existing wastewater treatment plant. The evaluation of the performance of these approach was based on biohydrogen yield and effluent quality. The simulations show high biohydrogen production rates, with picks during the summer months, while most of the effluent environmental parameters remain at the same or even lower levels compared with the currently used technology
The subgroup growth spectrum of virtually free groups
For a finitely generated group denote by the growth
coefficient of , that is, the infimum over all real numbers such
that . We show that the growth coefficient of a virtually
free group is always rational, and that every rational number occurs as growth
coefficient of some virtually free group. Moreover, we describe an algorithm to
compute
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