On the order of the unitary subgroup of a modular group algebra. (English) Zbl 0952.16022

In the paper under review the authors count the number of symmetric units in the group algebra \(KG\) for \(K\) being a finite field and \(G\) being a finite \(p\)-group. A unit \(u\) is called symmetric if the involution of the canonical Hopf algebra structure of \(KG\) fixes \(u\). The authors obtain a complete formula for \(G\) being an extraspecial \(2\)-group of order \(2^{2n+1}\), a central product of such a group with a cyclic group of order 4 and a \(2\)-group having an Abelian subgroup of index 2.


16U60 Units, groups of units (associative rings and algebras)
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
16S34 Group rings
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