BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center. We prove a theorem that suggests that this is the only limitation to obtain a non-abelian free group from a given Bass cyclic unit. More precisely, we prove that if u is a Bass cyclic unit of an integral group ring ZG of a solvable and finite group G, such that u has infinite order modulo the center of U(ZG) and it is based on an element of prime order, then there is a non-abelian free group generated by a power of u and a power of a unit in ZG which is either a Bass cyclic unit or a bicyclic unit.

ALTERNATING UNITS AS FREE FACTORS IN THE GROUP OF UNITS OF INTEGRAL GROUP RINGS

Let G be a group of odd order that contains a non-central element x whose order is either a prime p >= 5 or 3(l), with l >= 2. Then, in U(ZG), the group of units of ZG, we can find an alternating unit u based on x, and another unit v, which can be either a bicyclic or an alternating unit, such that for all sufficiently large integers m we have that < u(m), v(m)> = < u(m)> * < v(m)> congruent to Z * Z.

Histological evaluation of chitosan-based biomaterials used for the correction of critical size defects in rat`s calvaria

Chitosan, a biopolymer obtained from chitin, and its derivates, such as chitosan hydrochloride, has been reported as wound healing accelerators and as possible bone substitutes for tissue engineering, and therefore these Substances could be relevant in dentistry and periodontology. The purpose of this investigation was to make a histological evaluation of chitosan and chitosan hydrochloride biomaterials (gels) used in the correction of critical size bone defects made in rat`s calvaria. Bone defects of 8 mm in diameter were surgically created in the calviria of 50 Holtzman (Rattus norvegicus) rats and filled with blood clot (control), low molecular weight chitosan, high molecular weight chitosan, low molecular weight chitosan hydrochloride, and high molecular weight chitosan hydrochloride, numbering 10 animals, divided into two experimental periods (15 and 60 days), for each biomaterial. The histological evaluation was made based on the morphology of the new-formed tissues in defect`s region, and the results indicated that there was no statistical difference between the groups when the new bone formation in the entire defect`s area were compared (p > 0.05) and, except in the control groups, assorted degrees of inflammation Could be Seen. In Conclusion, chitosan and chitosan hydrochloride biomaterials used in this study were not able to promote new bone formation in critical size defects made in rat`s calvaria. (C) 2009 Wiley Periodicals, Inc. J Biomed Mater Res 93A: 107-114, 2016