Every Moufang loop of odd order with nontrivial commutant has nontrivial center

2013 ◽  
Vol 100 (6) ◽  
pp. 507-519 ◽  
Author(s):  
Piroska Csörgő
Keyword(s):  
Moufang Loop ◽  
Odd Order ◽  
Nontrivial Center

CLASSIFICATION OF MINIMAL NONASSOCIATIVE MOUFANG LOOPS OF ORDER pq3

2013 ◽  
Vol 23 (08) ◽  
pp. 1895-1908 ◽  
Author(s):  
WING LOON CHEE ◽  
STEPHEN M. GAGOLA ◽  
ANDREW RAJAH
Keyword(s):  
Abelian Group ◽  
Open Problem ◽  
Related Question ◽  
Moufang Loop ◽  
The Third ◽  
Odd Order ◽  
Moufang Loops ◽  
Mod P

An open problem in the theory of Moufang loops is to classify those loops which are minimally nonassociative, that is, loops which are nonassociative but where all proper subloops are associative. A related question is to classify all integers n for which a minimally nonassociative loop exists. In [Possible orders of nonassociative Moufang loops, Comment. Math. Univ. Carolin.41(2) (2000) 237–244], O. Chein and the third author showed that a minimal nonassociative Moufang loop of order 2q3can be constructed by using a non-abelian group of order q3. In [Moufang loops of odd order pq3, J. Algebra235 (2001) 66–93], the third author also proved that for odd primes p < q, a nonassociative Moufang loop of order pq3exists if and only if q ≡ 1 ( mod p). Here we complete the classification of minimally nonassociative Moufang loops of order pq3for primes p < q.

A characterization of nilpotent Moufang loops of odd order

2016 ◽  
Vol 15 (10) ◽  
pp. 1650183
Author(s):  
Piroska Csörgő
Keyword(s):  
Direct Product ◽  
Moufang Loop ◽  
Odd Order ◽  
Moufang Loops ◽  
Coprime Order

Glauberman and Wright in [G. G. Glauberman and C. R. B. Wright, Nilpotence of finite Moufang 2-loops, J. Algebra 8 (1968) 415–417] proved that a nilpotent Moufang loop is the direct product of [Formula: see text]-loops for some primes [Formula: see text], consequently the elements of coprime order commute in a nilpotent Moufang loop. In this paper, we prove that in Moufang loops of odd order this condition is equivalent to the central nilpotence.

ON FINITE p-GROUPS OF ODD ORDER WITH MANY SUBGROUPS 2-SUBNORMAL

1996 ◽  
Vol 24 (8) ◽  
pp. 2707-2719
Author(s):  
Gemma Parmeggiani ◽  
G. Zacher
Keyword(s):  
Odd Order

A CHARACTERISATION OF CERTAIN FINITE GROUPS OF ODD ORDER

2011 ◽  
Vol 111 (-1) ◽  
pp. 67-76
Author(s):  
Ashish Kumar Das ◽  
Rajat Kanti Nath
Keyword(s):  
Finite Groups ◽  
Odd Order

scholarly journals New Results for Oscillation of Solutions of Odd-Order Neutral Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1095
Author(s):  
Clemente Cesarano ◽  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Nawal A. Alshehri ◽  
Sayed K. Elagan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Odd Order ◽  
Future Prediction ◽  
Functional Differential ◽  
Delay Differential

Differential equations with delay arguments are one of the branches of functional differential equations which take into account the system’s past, allowing for more accurate and efficient future prediction. The symmetry of the equations in terms of positive and negative solutions plays a fundamental and important role in the study of oscillation. In this paper, we study the oscillatory behavior of a class of odd-order neutral delay differential equations. We establish new sufficient conditions for all solutions of such equations to be oscillatory. The obtained results improve, simplify and complement many existing results.

Lidstone-based collocation splines for odd-order BVPs

2020 ◽  
Author(s):  
F.A. Costabile ◽  
M.I. Gualtieri ◽  
A. Napoli
Keyword(s):  
Odd Order

scholarly journals Oscillation and non-oscillation of some neutral differential equations of odd order

1992 ◽  
Vol 15 (3) ◽  
pp. 509-515 ◽  
Author(s):  
B. S. Lalli ◽  
B. G. Zhang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solution ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations ◽  
Neutral Term ◽  
Odd Order ◽  
Existence Criterion ◽  
Oscillation Of Solutions

An existence criterion for nonoscillatory solution for an odd order neutral differential equation is provided. Some sufficient conditions are also given for the oscillation of solutions of somenth order equations with nonlinearity in the neutral term.

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