The character table of the fully nonrigid water cluster (cyclic forms), (H_{2}O){_i}, with C{_ih} symmetry derived for the first time, for 2<=i <=6. The group of all feasible permutations is the wreath product of groups S{_i}[S{_2}] which consists of i!2i operations for i = 2, ..., 6 divided into ( w.r.t) 5, 10, 20, 36, 65 conjugacy classes and 5, 10, 20, 36, 65 irreducible representations resp...

If a group ( G ) of order pm contains only one subgroup of order pa, a > 0, it is known to be cyclic unless both p = 2 and at = l.f In this special case there are two possible groups whenever m > 2. The number of cyclic subgroups of order pa in G is divisible by p whenever G is non-cyclic and p > 2. J In the present paper we shall consider the possible types of G when it is assumed that there a...

finite affine groups are given by groups of translations and di-lations on finite cyclic groups. for cyclic groups of prime orderwe develop a time-scale (wavelet) analysis and show that for alarge class of non-zero window signals/vectors, the generatedfull cyclic wavelet system constitutes a frame whose canonicaldual is a cyclic wavelet frame.

In a group G, we denote the (cyclic) group of powers of some g ∈ G by 〈g〉 = {g : k ∈ Z}. If G = 〈g〉, then G itself is cyclic, with g as a generator. Examples of infinite cyclic groups include Z, with (additive) generator 1, and the group 2Z of integral powers of the real number 2, with generator 2. The most basic examples of finite cyclic groups are Z/(m) with (additive) generator 1 and μm = {z...

anti-müllerian hormone (amh) has been observed to decrease with the development of hemorrhagic anovulatory follicles (hafs) in mares. two studies were conducted to evaluate amh concentration in mares with hafs compared to seasonally anoestrous and cyclic mares, and to elucidate changes of amh with the development of luteinised unruptured follicles (lufs). in study 1, amh and progesterone were e...

We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1, 1)-knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the n-fold stronglycyclic branched coverings of (1, 1)-knots, through the elements of the mapping class group. We prove that every n-fold stro...

We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1, 1)-knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the n-fold stronglycyclic branched coverings of (1, 1)-knots, through the elements of the mapping class group. We prove that every n-fold stro...

We show that soluble groups G of type Bredon-FP∞ with respect to the family of all virtually cyclic subgroups of G are always virtually cyclic. In such a group centralizers of elements are of type FP∞. We show that this implies the group is polycyclic. Another important ingredient of the proof is that a polycyclic-by-finite group with finitely many conjugacy classes of maximal virtually cyclic ...

Ikegami and Saeki have proved that the cobordism group of Morse functions on oriented surfaces is an infinite cyclic group. Their method is applicable with a little modification to the computation of the cobordism group of Morse functions on unoriented surfaces. We prove that this group is isomorphic to the direct sum of the infinite cyclic group and the finite group of order two.