Minimal Number of Generators and Minimum Order of a Non-Abelian Group Whose Elements Commute with Their Endomorphic Images
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چکیده
منابع مشابه
Minimal Number of Generators and Minimum Order of a Non-Abelian Group whose Elements Commute with Their Endomorphic Images
A group in which every element commutes with its endomorphic images is called an E-group. If p is a prime number, a p-group G which is an E-group is called a pE-group. Every abelian group is obviously an E-group. We prove that every 2-generator E-group is abelian and that all 3-generator E-groups are nilpotent of class at most 2. It is also proved that every infinite 3-generator E-group is abel...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2008
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870801941903