Group algebras whose p-elements form a subgroup
نویسندگان
چکیده
منابع مشابه
Group Algebras Whose Involutory Units Commute
Abstract. Let K be a field of characteristic 2 and G a nonabelian locally finite 2-group. Let V (KG)be the group of units with augmentation 1 in the group algebra KG. An explicit list of groups is given, and it is proved that all involutions in V (KG) commute with each other if and only if G is isomorphic to one of the groups on this list. In particular, this property depends only on G and not ...
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A p-group is called powerful if every commutator is a product of p th powers when p is odd and a product of fourth powers when p = 2. In the group algebra of a group G of p-power order over a finite field of characteristic p, the group of normalized units is always a p-group. We prove that it is never powerful except, of course, when G is abelian.
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Let U(KλG) be the group of units of an infinite twisted group algebra KλG over a field K. We describe the maximal FC-subgroup of U(KλG) and give a characterization of U(KλG) with finitely conjugacy classes. In the case of group algebras we obtain the Cliff-Sehgal-Zassenhaus’ theorem.
متن کاملGroups of Order 2 Whose Squared Elements Constitute a Cyclic Subgroup.
1 The first four notes of this series appeared in these PROCEEDINGS, 14, 915-918 (1928); 15, 41-42 (1929); 16, 594-598 (1930); 17, 376-380 (1931). In these notes we were concerned exclusively with the methods of Hausdorff and Woronoi-Norlund. The results of the present note were communicated to the American Mathematical Society on April 14, 1933. Cf. also E. Hille, "Summation of Fourier Series,...
متن کاملEuler characteristics and Möbius algebras of p-subgroup categories
In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t Let G be a finite group and p a prime number. We compute the Euler characteristic in the sense of Leinster f...
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ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2016
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498817501705