ALMOST ALL EXTRASPECIAL p-GROUPS ARE SWAN GROUPS
نویسنده
چکیده
Let P be an extraspecial p-group which is neither dihedral of order 8, nor of odd order p and exponent p. Let G be a finite group having P as a Sylow p-subgroup. Then the mod-p cohomology ring of G coincides with that of the normalizer NG(P ).
منابع مشابه
The Dade group of (almost) extraspecial p-groups
In this paper, we determine a presentation by explicit generators and relations for the Dade group of all (almost) extraspecial p-groups. The proof of the main result uses the cohomological properties of the Tits building corresponding to the natural geometric structure of the lattice of subgroups of such p-groups. AMS Subject Classification : 20C20, 20D15
متن کاملar X iv : 0 70 6 . 17 61 v 1 [ qu an t - ph ] 1 2 Ju n 20 07 From Extraspecial Two - Groups To GHZ states
In this paper we explore natural connections among extraspecial 2-groups, almost-complex structures, unitary representations of the braid group and the Greenberger-Horne-Zeilinger (GHZ) states. We first present new representations of extraspecial 2-groups in terms of almost-complex structures and use them to derive new unitary braid representations as extensions of representations of the extras...
متن کاملAn Efficient Quantum Algorithm for the Hidden Subgroup Problem in Extraspecial Groups
Extraspecial groups form a remarkable subclass of p-groups. They are also present in quantum information theory, in particular in quantum error correction. We give here a polynomial time quantum algorithm for finding hidden subgroups in extraspecial groups. Our approach is quite different from the recent algorithms presented in [17] and [2] for the Heisenberg group, the extraspecial p-group of ...
متن کاملFrom Extraspecial Two-Groups To GHZ States
In this paper we explore natural connections among extraspecial 2-groups, almost-complex structures, unitary representations of the braid group and the Greenberger-Horne-Zeilinger (GHZ) states. We first present new representations of extraspecial 2-groups in terms of almost-complex structures and use them to derive new unitary braid representations as extensions of representations of the extras...
متن کاملua nt - p h / 07 01 23 5 v 1 3 1 Ja n 20 07 An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups ∗
Extraspecial groups form a remarkable subclass of p-groups. They are also present in quantum information theory, in particular in quantum error correction. We give here a polynomial time quantum algorithm for finding hidden subgroups in extraspecial groups. Our approach is quite different from the recent algorithms presented in [17] and [2] for the Heisenberg group, the extraspecial p-group of ...
متن کامل