Presentations for Unit Groups of Modular Group Algebras of Groups of Order 16
نویسنده
چکیده
For a p-group G and the field F of p elements, let V denote the group of normalized units of the group algebra F G . Generators and relations are provided for V for each group G of order dividing 16. The presentations are sufficiently concise to permit transcription for machine calculation with V . Some applications are described. A theoretical method for obtaining presentations for V is developed. It is most effective when p = 2 , or when p = 3 and the commutator subgroup G' is of order 3. Implementation involves extensive calculation in F G .
منابع مشابه
AUTOMORPHISM GROUP OF GROUPS OF ORDER pqr
H"{o}lder in 1893 characterized all groups of order $pqr$ where $p>q>r$ are prime numbers. In this paper, by using new presentations of these groups, we compute their full automorphism group.
متن کاملWreath Products in the Unit Group of Modular Group Algebras of 2-groups of Maximal Class
We study the unit group of the modular group algebra KG, where G is a 2-group of maximal class. We prove that the unit group of KG possesses a section isomorphic to the wreath product of a group of order two with the commutator subgroup of the group G. MSC2000: Primary 16S34, 20C05; Secondary 16U60
متن کاملWreath Products in Modular Group Algebras of Some Finite 2-groups
Let K be field of characteristic 2 and let G be a finite nonabelian 2-group with the cyclic derived subgroup G′, and there exists a central element z of order 2 in Z(G)\G′. We prove that the unit group of the group algebra KG possesses a section isomorphic to the wreath product of a group of order 2 with the derived subgroup of the group G, giving for such groups a positive answer to the questi...
متن کاملA classification of hull operators in archimedean lattice-ordered groups with unit
The category, or class of algebras, in the title is denoted by $bf W$. A hull operator (ho) in $bf W$ is a reflection in the category consisting of $bf W$ objects with only essential embeddings as morphisms. The proper class of all of these is $bf hoW$. The bounded monocoreflection in $bf W$ is denoted $B$. We classify the ho's by their interaction with $B$ as follows. A ``word'' is a function ...
متن کاملThe Unit Group of Small Group Algebras and the Minimum Counterexample to the Isomorphism Problem
Let KG denote the group algebra of the group G over the field K and let U(KG) denote its group of units. Here without the use of a computer we give presentations for the unit groups of all group algebras KG, where the size of KG is less than 1024. As a consequence we find the minimum counterexample to the Isomorphism Problem for group algebras. AMS Subject Classification: 16S34, 16U60, 20C05
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010