지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
초록· 키워드
오류제보하기
Let x be an element of a group G and be an automorphism of G. Then for a positive integer n, the autocommutator [x,n α] is defined inductively by [x, α] = x−1xα = x−1α(x) and [x,n+1 α] = [[x,n α], α]. We call the group G to be n-auto-Engel if [x,n α] = [α,n x] = 1 for all x ∈ G and every α ∈ Aut(G), where [α, x] = [x, α]−1. Also, for any integer n 6= 0, 1, a group G is called an n-auto-Bell group when [xn, α] = [x,αn] for every x ∈ G and each α ∈ Aut(G). In this paper, we investigate the properties of such groups and show that if G is an n-auto-Bell group, then the factor group G/L3(G) has finite exponent dividing 2n(n − 1), where L3(G) is the third term of the upper autocentral series of G. Also, we give some examples and results about n-auto-Bell abelian groups.
목차
등록된 정보가 없습니다.
참고문헌 (13)
참고문헌 신청
A. R. Jamali / 2002 / Some new non-abelian 2-groups with abelian automorphism groups / J. Group Theory 5 (1) : 53 ~ 57
A. Tortora / 2009 / Some properties of Bell groups / Comm. Algebra 37 (2) : 431 ~ 438
C. Delizia / 2006 / The structure of Bell groups / J. Group Theory 9 (1) : 117 ~ 125
D. J. S. Robinson / 1972 / Finiteness Conditions and Generalized Soluble Groups, Parts 1 and 2 / Springer-Verlag
L. -C. Kappe / 1988 / Groups with 3-abelian normal closures / Arch. Math. (Basel) 51 (2) : 104 ~ 110
A. Tortora / 2009 / Some properties of Bell groups / Comm. Algebra 37 (2) : 431 ~ 438
C. Delizia / 2006 / The structure of Bell groups / J. Group Theory 9 (1) : 117 ~ 125
D. J. S. Robinson / 1972 / Finiteness Conditions and Generalized Soluble Groups, Parts 1 and 2 / Springer-Verlag
L. -C. Kappe / 1988 / Groups with 3-abelian normal closures / Arch. Math. (Basel) 51 (2) : 104 ~ 110
이 논문의 저자 정보
최근 본 자료
댓글(0)
0