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ABSTRACT It is known that if a group G has an abelian subgroup of finite index n, then it contains an abelian characteristic subgroup A of index at most nn.… Click to show full abstract
ABSTRACT It is known that if a group G has an abelian subgroup of finite index n, then it contains an abelian characteristic subgroup A of index at most nn. The aim of this paper is to improve this bound by showing that the characteristic subgroup A can be chosen of index at most n2. Examples prove that this bound is the best possible. Our main result is obtained as an application of a general method for the construction of large characteristic subgroups.
Keywords:
subgroup;
index;
large characteristic;
note large;
characteristic subgroups
Journal Title: Communications in Algebra
Year Published: 2018
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Journal Title: Communications in Algebra
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!