کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6414328 1630461 2016 33 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Cyclic complements and skew morphisms of groups
ترجمه فارسی عنوان
تکمیلی سیکلی و مورفیسم های مبهم گروه
کلمات کلیدی
گروه محدود فاکتور سازی، محصول زیرگروه ها، زیرمجموعه های تکمیلی، مورفیسم پیچک،
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

A skew morphism of a group is a generalisation of an automorphism, arising in the context of regular Cayley maps or of groups expressible as a product AB of subgroups A and B with B cyclic and A∩B={1}. A skew morphism of a group A is a bijection φ:A→A fixing the identity element of A and having the property that φ(xy)=φ(x)φπ(x)(y) for all x,y∈A, where π(x) depends only on x. The kernel of φ is the subgroup of all x∈A for which π(x)=1.In this paper, we present a number of previously unknown properties of skew morphisms, one being that if A is any finite group, then the order of every skew morphism of A is less than |A|, and another being that the kernel of every skew morphism of a non-trivial finite group is non-trivial. We also prove a number of theorems about skew morphisms of finite abelian groups, some of which simplify or extend recent theorems of Kovács and Nedela [13]. For example, we determine all skew morphisms of the finite abelian groups whose order is prime, or the square of a prime, or the product of two distinct primes. In addition, we completely determine the finite abelian groups for which every skew morphism is an automorphism.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 453, 1 May 2016, Pages 68-100
نویسندگان
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