Quasiregular Groups Research Articles

Finite nilpotent algebras with metacyclic quasiregular group

We present a classification of finite milpotent algebras with metacyclic quasiregular group.

Quasi-regular eutectic growth: A study of the solidification of some high volume-fraction faceted phase anomalous eutectics

The work reported here is a continuation of the development of a morphological classification scheme for binary eutectics based on the structure of the solid/liquid interface of each eutectic phase. The interest was centered on the so-called quasi-regular group of eutectics in which the volume fraction ( V F) of the faceted phase exceeds 50%. The effects of temperature gradient, in both the liquid ( G L) and the solid ( G S), and growth rate on a number o quasi-regular eutectics were investigated. The morphologies of unidirectionally grown Bi-Cd, Sb-Cu 2Sb and Bi-Au 2Bi eutectics were studied in detail. The structural degradation and the growth forms of the primary crystals of the minor eutectic phases in alloys of near eutectic composition were also examined in order to arrive at a more comprehensive view of quasi-regular growth. From the detailed microscopic observations made, it was found that the quasi-regular eutectic morphology can be influenced by the growth direction and G S, but not by G L. The primary crystals of the minor eutectic phase near the eutectic composition undergo solution growth as the volume fraction of that phase decreases.

Semiperfect rings with nilpotent quasiregular group

Semiperfect rings with nilpotent quasiregular group

Quasi regular groups of finite commutative nilpotent algebras

Quasi regular groups of finite commutative nilpotent algebras

Correction to: “On ring structures determined by groups”

PROOF. Lemma 2, we know that R=RTGRF, where RT is the torsion ideal of R and RF is the torsion-free ideal of R. Hence R/J -RT/JTERF/JF. But then RF/JF is a torsion which implies that RF = JF, since +RF is a torsion-free divisible group. Hopkin's Theorem [4 ] then forces RF=JF =O, and R is therefore a torsion In addition, Professor S. K. Jain has kindly made me aware of two errors of omission. The last line of Theorem 1 should read X 2 matrices over GF(2) or GF(3)., and lines 6 and 7 of the proof should read. . ... Furthermore, the 2 X 2 matrix rings over GF(2) and GF(3) are the only matrix rings with a solvable. The following should be added to the statement of Corollary 2 of Theorem 1: A of type (a) may occur as a direct summand with rings of types (b), (c), and (d), since its quasi-regular group has order 1. ADDED IN PROOF. The paragraph preceding Corollary 1 on p. 473 should now read: Since the quasi-regular group of the of 2X2 matrices over GF(2) or GF(3) is not nilpotent, we have the following corollary to Theorem 1. The line following the first paragraph on p. 474 should be deleted, while the first sentence in the proof of Theorem 2 (p. 475) should now read: By Propositions 2' and 3, R is a torsion ring. REMARK. P. B. Battacharya and S. K. Jain obtained essentially the same results in A note on the adjoint group of a ring (to appear in Archive der Mathematik) using different techniques. They extended these results in Rings having solvable adjoint groups (to appear in these Proceedings) where they prove: If R is a perfect and 'R is a finitely generated solvable group then R is finite, and and hence 'R = P, o P2 0 0 . . O Pm where the Pi are pairwise commuting p-groups. (Hyman Bass first defined perfect rings in Trans. Amer. Math. Soc. 95 (1960), 466-488.)

On ring structures determined by groups

In this paper we show that part of the structure of an artinian ring is determined when it has a solvable, simple, nilpotent, supersolvable, torsion, or finitely generated quasi-regular group. For the case of a simple quasi-regular group, the rings are completely described. We also give an application of our results to finite dimensional group algebras. Our proofs depend, in part, on properties of matrix algebras over division rings and the following two known lemmas.

Artinian rings with a cyclic quasi-regular group

Artinian rings with a cyclic quasi-regular group