scholarly journals Endomorphism rings and direct sums of torsion free abelian groups

1975 ◽  
Vol 211 ◽  
pp. 225-225 ◽  
Author(s):  
D. M. Arnold ◽  
E. L. Lady
Keyword(s):  
Abelian Groups ◽  
Endomorphism Rings ◽  
Direct Sums ◽  
Free Abelian Groups ◽  
Torsion Free

scholarly journals Automorphisms of nilpotent groups of class two with small rank

1985 ◽  
Vol 39 (1) ◽  
pp. 121-131 ◽  
Author(s):  
Thomas A. Fournelle
Keyword(s):  
Automorphism Groups ◽  
Abelian Groups ◽  
Nilpotent Groups ◽  
Factor Group ◽  
Direct Sums ◽  
Matrix Computations ◽  
Central Factor ◽  
Rank One ◽  
Free Abelian Groups ◽  
Torsion Free

AbstractRational abelian groups, that is, torsion-free abelian groups of rank one, are characterized by their types. This paper characterizes rational nilpotent groups of class two, that is, nilpotent groups of class two in which the center and central factor group are direct sums of rational abelian groups. This characterization is done according to the types of the summands of the center and the central factor group. Using these types and some cohomological techniques it is possible to determine the automorphism group of the nilpotent group in question by performing essentially matrix computations.In particular, the automorphism groups of rational nilpotent groups of class two and rank three are completely described. Specific examples are given of semicomplete and pseudocomplete nilpotent groups.

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