Search results for "Abelian group"

Tangential Hilbert problem for perturbations of hyperelliptic Hamiltonian systems

1999

The tangential Hilbert 16th problem is to place an upper bound for the number of isolated ovals of algebraic level curves { H ( x , y ) = const } \{H(x,y)=\operatorname {const}\} over which the integral of a polynomial 1-form P ( x , y ) d x + Q ( x , y ) d y P(x,y)\,dx+Q(x,y)\,dy (the Abelian integral) may vanish, the answer to be given in terms of the degrees n = deg ⁡ H n=\deg H and d = max ( deg ⁡ P , deg ⁡ Q ) d=\max (\deg P,\deg Q) . We describe an algorithm producing this upper bound in the form of a primitive recursive (in fact, elementary) function of n n and d d for the particular case of hyperelliptic polynomials H ( x , y ) = y 2 + U ( x ) H(x,y)=y^2+U(x) under the additional as…

Hyper-abelian groups with finite co-central rank

2004

AbstractA group G has finite co-central rank s if there exists a least non-negative integer s such that every finitely generated subgroup H can be generated by at most s elements modulo the centre of H. The investigation of such groups has been started in [J.P. Sysak, A. Tresch, J. Group Theory 4 (2001) 325]. It is proved that hyper-abelian groups with finite co-central rank are locally soluble. The interplay between the Prüfer rank condition, the condition of having finite abelian section rank and the finite co-central rank condition is studied. As one result, a hyper-abelian group G with finite co-central rank has an ascending series with abelian factors of finite rank and every chief fac…

Metric properties of the group of area preserving diffeomorphisms

2001

Area preserving cliffeoinorpliisms of the 2-disk which are identity near the boundary form a group D2 wllich can be equipped, usin-g tlhe L2nlorm on its Lie algebra, with a right invariant metric. Witll tllis metric the diameter of D2 is infinite. In this paper we sl-iow that D2 contains quasiisometric embeddings of any finitely generated free group and any finitely generated abelian free group.

Two groups with isomorphic group algebras

1990

Invariant ordering of surface groups and 3-manifolds which fibre over $S^1$

2006

Sylow normalizers and character tables, II

2002

Suppose thatG is a finitep-solvable group and letPe Syl p (G). In this note, we prove that the character table ofG determines ifN G(itP)/P is abelian.

On groups with abelian Sylow 2-subgroups

1970

Finite groups with abelian Sylow 2-subgroups have been classified by Walter [8]. In this note I want to describe an alternate proof of some partial result of Walter's work, namely the theorem stated below. It represents the first major reduction step in that classification. The approach used here is to some extent derived from [1]. ! Besides the groups L 2 (q)= PSL(2, q) another class of simple groups enters our discussion: We say that a simple group G with abelian Sz-subgroups is of type JR (Janko-Ree) if, for any involution t in G, CG (t) is a maximal subgroup of G isomorphic to ( t ) | E where PSL(2, q)~ E ~_ PFL(2, q) with odd q > 5. In fact, E = L 2 (q), as proved by Walter 1-7] ; and …

On James Hyde's example of non-orderable subgroup of $\mathrm{Homeo}(D,\partial D)$

2020

In [Ann. Math. 190 (2019), 657-661], James Hyde presented the first example of non-left-orderable, finitely generated subgroup of $\mathrm{Homeo}(D,\partial D)$, the group of homeomorphisms of the disk fixing the boundary. This implies that the group $\mathrm{Homeo}(D,\partial D)$ itself is not left-orderable. We revisit the construction, and present a slightly different proof of purely dynamical flavor, avoiding direct references to properties of left-orders. Our approach allows to solve the analogue problem for actions on the circle.

On 2-groups with no abelian subgroups of rank four

1975

The complex of words and Nakaoka stability

2005

We give a new simple proof of the exactness of the complex of injective words and use it to prove Nakaoka's homology stability for symmetric groups. The methods are generalized to show acyclicity in low degrees for the complex of words in "general position". Hm(§ni1;Z) = Hm(§n;Z) for n=2 > m where §n denotes the permutation group of n elements. An elementary proof of this fact has not been available in the literature. In the first section the complex C⁄(m) of abelian groups is studied which in de- gree n is freely generated by injective words of length n. The alphabet consists of m letters. The complex C⁄(m) has the only non vanishing homology in degree m (Theorem 1). This is a result of F.…