کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
11024740 | 1701072 | 2018 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
FC-groups with finitely many automorphism orbits
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
Let G be a group. The orbits of the natural action of Aut(G) on G are called “automorphism orbits” of G, and the number of automorphism orbits of G is denoted by Ï(G). In this paper we prove that if G is an FC-group with finitely many automorphism orbits, then the derived subgroup Gâ² is finite and G admits a decomposition G=Tor(G)ÃD, where Tor(G) is the torsion subgroup of G and D is a divisible characteristic subgroup of Z(G). We also show that if G is an infinite FC-group with Ï(G)⩽8, then either G is soluble or Gâ
A5ÃH, where H is an infinite abelian group with Ï(H)=2. Moreover, we describe the structure of the infinite non-soluble FC-groups with at most eleven automorphism orbits.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 516, 15 December 2018, Pages 401-413
Journal: Journal of Algebra - Volume 516, 15 December 2018, Pages 401-413
نویسندگان
Raimundo A. Bastos, Alex C. Dantas,