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Abstract Let G be a finite p-group, and let F be a field of characteristic p. C. Bagiński proved that if is cyclic of order pn, then the derived length… Click to show full abstract
Abstract Let G be a finite p-group, and let F be a field of characteristic p. C. Bagiński proved that if is cyclic of order pn, then the derived length of the group of units of the group algebra FG is equal to , provided that p > 2. In this paper, we show that, for p = 2, the same equality holds if and only if or the nilpotency class of G is at most n. Applying this result, we classify the nilpotent torsion 2-abelian groups whose group algebras have solvable group of units with maximal derived length.
Keywords:
group units;
whose group;
units maximal;
group algebras;
derived length;
group
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!