A bipartite monoid is a commutative monoid Q together with an identified subset P ⊂ Q. In this paper we study a class of bipartite monoids, known as misère quotients, that are naturally associated to impartial combinatorial games. We introduce a structure theory for misère quotients with |P| = 2, and give a complete classification of all such quotients up to isomorphism. One consequence is that...

CONTENTS This article proposes to represent subgroups of finitely presented 1 . Creation of Quotient Representations and Easy Calculations g r o u p s b y t h e i r i m a g e i n a quo t ient. It gives algorithms for basic 2. Subdirect Products operations in this representation and investigates how iteration 3. Iterated Quotient Representations of this approach can be used to extend known quoti...

A C *-algebra A is called an ideal C * -algebra (or equally a dual algebra) if it is an ideal in its bidual A**. M.C.F. Berglund proved that subalgebras and quotients of ideal C*-algebras are also ideal C*-algebras, that a commutative C *-algebra A is an ideal C *-algebra if and only if it is isomorphicto C (Q) for some discrete space ?. We investigate ideal J*-algebras and show that the a...

We study the Modular Isomorphism Problem for groups of small order based on an improvement algorithm described by Eick. Our allows to determine quotients I(kG)/I(kG)m augmentation ideal without first computing full I(kG). computations yield a positive answer MIP 37 and strongly reduce cases that need be checked 56. also show counterexamples found recently García-Lucas, Margolis del Río are only...

Baer characterized capable finite abelian groups (a group is capable if it is isomorphic to the quotient of some group by its center) by a condition on the size of the factors in the invariant factor decomposition (the group must be noncyclic and the top two invariant factors must be equal). We provide a different characterization, given in terms of a condition on the lattice of subgroups. Name...

Quotienting by simulation equivalences is awell-established technique for reducing the size of nondeterministic Büchi automata.We adapt this technique to alternating Büchi automata. To this end we suggest two new quotients, namely minimax and semi-elective quotients, prove that they preserve the recognized languages, and show that computing them is not more difficult than computing quotients fo...

We propose an approach via Frobenius manifolds to the study (began in [BCK2]) of the relation between rational Gromov-Witten invariants of nonabelian quotients X//G and those of the corresponding “abelianized” quotients X//T, for T a maximal torus in G. The ensuing conjecture expresses the Gromov-Witten potential of X//G in terms of the potential of X//T. We prove this conjecture when the nonab...

We discuss quotients of Anti-de Sitter (AdS) spacetime by a discrete group in light of the AdS-CFT correspondence. Some quotients describe closed universes which expand from zero volume to a maximum size and then contract. Maldacena's conjecture suggests that they should be represented in string theory by suitable quotients of the boundary conformal eld theory. We discuss the required identi ca...

We discuss quotients of Anti-de Sitter (AdS) spacetime by a discrete group in light of the AdS-CFT correspondence. Some quotients describe closed universes which expand from zero volume to a maximum size and then contract. Maldacena’s conjecture suggests that they should be represented in string theory by suitable quotients of the boundary conformal field theory. We discuss the required identif...