If a finite abelian group G is a direct product of its subsets such that G = A1···Ai···An, G is said to have the Hajos-n-proprty if it follows that one of these subsets, say Ai is periodi...If a finite abelian group G is a direct product of its subsets such that G = A1···Ai···An, G is said to have the Hajos-n-proprty if it follows that one of these subsets, say Ai is periodic, meaning that there exists a nonidentity element g in G such that gAi = Ai . Using some properties of cyclotomic polynomials, we will show that the cyclic groups of orders pα and groups of type (p2,q2) and (pα,pβ) where p and q are distinct primes and α, β integers ≥ 1 have this property.展开更多
Hajos' conjecture asserts that a simple eulerian graph on n vertices can be decomposed into at most n-1/2 circuits,In this paper,we propose a new conjecture which is equivalent to Hajos' conjecture.and show th...Hajos' conjecture asserts that a simple eulerian graph on n vertices can be decomposed into at most n-1/2 circuits,In this paper,we propose a new conjecture which is equivalent to Hajos' conjecture.and show that to prove Hajos' conjecture,it is sufficent to prove this new conjecture for 3-connected graphs.Furthermore,a special 3-cut is considered also.展开更多
文摘If a finite abelian group G is a direct product of its subsets such that G = A1···Ai···An, G is said to have the Hajos-n-proprty if it follows that one of these subsets, say Ai is periodic, meaning that there exists a nonidentity element g in G such that gAi = Ai . Using some properties of cyclotomic polynomials, we will show that the cyclic groups of orders pα and groups of type (p2,q2) and (pα,pβ) where p and q are distinct primes and α, β integers ≥ 1 have this property.
基金This research is partially supported by the National Postdoctoral Fund of China and Natural Science Foundation of China(No. 10001035) This work was finished while the author was working for Academy of Mathematics and Systems Science, Chinese of Academy
文摘Hajos' conjecture asserts that a simple eulerian graph on n vertices can be decomposed into at most n-1/2 circuits,In this paper,we propose a new conjecture which is equivalent to Hajos' conjecture.and show that to prove Hajos' conjecture,it is sufficent to prove this new conjecture for 3-connected graphs.Furthermore,a special 3-cut is considered also.
