We construct an example of a torsion free freely indecomposable finitely presented nonquasiconvex subgroup H of a word hyperbolic group G such that the limit set of G is not the limit set of a quasiconvex subgroup of G. In particular, this gives a counterexample to the conjecture of G.Swarup that a finitely presented one-ended subgroup of a word hyperbolic group is quasiconvex if and only if it...

Given a set r of permutations of an n-set, let G be the group of permutations generated by r. I f p is any prime, it is known that a Sylow p-subgroup P of G can be found in polynomial time. We show that the normalizer of P can also be found in polynomial time. In particular, given two Sylow p-subgroups of G, all elements conjugating one to the other can be found (as a coset of the normalizer of...

Quantum normalizer circuits were recently introduced as generalizations of Clifford circuits [1]: a normalizer circuit over a finite Abelian group G is composed of the quantum Fourier transform (QFT) over G, together with gates which compute quadratic functions and automorphisms. In [1] it was shown that every normalizer circuit can be simulated efficiently classically. This result provides a n...

In this study, firstly, we interpret the level set, support, kernel for bipolar complex fuzzy (BCF) characteristic function, and BCF point. Then, subgroup, normal conjugate, normalizer cosets, abelian factor group. Furthermore, present associated examples theorems, prove these theorems. After that, image pre-image of subgroups under homomorphism related

The novel notion of rigid commutators is introduced to determine the sequence logarithms indices a certain normalizer chain in Sylow 2-subgroup symmetric group on 2^n letters. terms this are proved be those partial sums partitions an integer into at least two distinct parts, that relates famous Euler's partition theorem.

In this paper, we show that for every abelian subgroup H of a Garside group, some conjugate gHg consists of ultra summit elements and the centralizer of H is a finite index subgroup of the normalizer of H. Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the algebraic flat torus theorem for Garside groups and solve several algorithmic problems conc...

We show that, given a saturated fusion system, it is, under certain conditions, possible to identify SL2(q) acting on a natural module inside the normalizer of an essential subgroup. In particular, this is the case if the fusion system is non-constrained and has only one conjugacy class of essential subgroups.

We improve a bound of Borcherds on the virtual cohomological dimension of the non-reflection part of the normalizer of a parabolic subgroup of a Coxeter group. Our bound is in terms of the types of the components of the corresponding Coxeter subdiagram rather than the number of nodes. A consequence is an extension of Brink’s result that the non-reflection part of a reflection centralizer is fre...

In this paper it is proven that if the group of covering translations of the covering space of a compact, connected, P-irreducible 3-manifold corresponding to a non-trivial, finitely-generated subgroup of its fundamental group is infinite, then either the covering space is almost compact or the subgroup is infinite cyclic and has normalizer a non-finitely-generated subgroup of the rational numb...