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Extraspecial p-groups

Saharon Shelah, Juris Steprāns
1987 Annals of Pure and Applied Logic  
It is shown that there is a class of cardinals 3-for which there are 2 x extraspecial p-groups of size 3. without abelian subgroups of size 3..  ...  [3.]2--> 2 it is possible to construct an extraspecial p-group.  ...  Introduction In his survey of FC-groups [7] Tomkinson poses some questions about extraspecial p-groups which will be answered in this paper.  ... 
doi:10.1016/0168-0072(87)90041-8 fatcat:6rzq5hqdujc4dflaf5haa7g2ai

Essential cohomology and extraspecial $p$-groups

Pham Anh Minh
2000 Transactions of the American Mathematical Society  
Let us recall that an extraspecial p-group G is of order p 2n+1 (n ∈ N) and is isomorphic to one of the following central products of groups: are extraspecial p-groups of order p 3 .  ...  Let p be an odd prime number and let G be an extraspecial pgroup.  ...  We are now interested in extraspecial p-groups G.  ... 
doi:10.1090/s0002-9947-00-02689-1 fatcat:6iuhcdrgjrbzzfzr2o6zrvoy4a

The Dade group of (almost) extraspecial p-groups

Serge Bouc, Nadia Mazza
2004 Journal of Pure and Applied Algebra  
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.  ...  We also thank Jon Carlson, who solved ÿrst the case of extraspecial groups of order p 3 .  ... 
doi:10.1016/j.jpaa.2004.02.008 fatcat:dtyitwwkqfb5lp6pqq5sb3vgbq

Almost all extraspecial p-groups are swan groups

David John Green, Pham Anh Minh
2000 Bulletin of the Australian Mathematical Society  
Let P be an extraspecial p-group which is neither dihedral of order 8, nor of odd order p^3 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 N_G(P).  ...  All extraspecial p-groups P apart from D s and E are Swan groups.  ... 
doi:10.1017/s0004972700018566 fatcat:dq6zngwenjar5k453hkzgfzxqm

Almost All Generalized Extraspecial p-Groups Are Resistant

Radu Stancu
2002 Journal of Algebra  
Let P be a generalized extraspecial p-group.  ...  Let P be a generalized extraspecial p-group.  ... 
doi:10.1006/jabr.2001.9069 fatcat:ct627phypvhr3h3k252bubqteu

Transfer and Chern classes for extraspecial p-groups

David J. Green, Pham Anh Minh
2008 arXiv   pre-print
In the cohomology ring of an extraspecial p-group, the subring generated by Chern classes and transfers is studied.  ...  Let p be an odd prime. For n ≥ 1, denote by P = P n the extraspecial p-group of order p 2n+1 and exponent p.  ...  Chern classes and extraspecial p-groups The integral (group) cohomology of the unitary group U (n) is a polynomial algebra with n generators.  ... 
arXiv:0809.2920v1 fatcat:d6m7tu7tzrbbpdz33mnukjrk6e

The K(n)-Euler characteristic of extraspecial p-groups

Maurizio Brunetti
2001 Journal of Pure and Applied Algebra  
Let p be an odd prime, and let K(n) * denote the nth Morava K-theory at the prime p; we compute the K(n)-Euler characteristic n;p(G) of the classifying space of an extraspecial p-group G.  ...  Equivalently, we get the number of conjugacy classes of commuting n-tuples in the group G.  ...  Let E m be an extraspecial p-group of order p 2m+1 .  ... 
doi:10.1016/s0022-4049(99)00102-4 fatcat:uegpqlzkwbb7raiyvayridvmfi

On the Conjugacy Search Problem in Extraspecial p-Groups [article]

Simran Tinani
2022 arXiv   pre-print
This paper demonstrates a polynomial time solution of the CSP in an important class of nonabelian groups, the extraspecial p-groups.  ...  The consequences of our results are practically relevant for ruling out several groups as platforms, since several nonabelian groups are constructed by combining smaller groups by taking direct and central  ...  Every extraspecial p-group has order p 1+2n and is a central product of n extraspecial groups of order p 3 .  ... 
arXiv:2203.03526v1 fatcat:b2znck2hjnfjtkglf4jikw7ad4

Mod p cohomology algebras of finite groups with extraspecial Sylow p-subgroups

Hiroki SASAKI
2000 Hokkaido Mathematical Journal  
INTRODUCTION The following p-groups are known as noncommutative p-groups that have cyclic $ma]\dot{o}mal$ subgroups: (1) $p=2$ , dihedral 2-group $D_{m}=\{x,y|x^{2^{m-1}}=y^{2}=1,yxy=x^{-1}$ ), $m\geq  ...  STRUCTURE OF $G$ Since the p-group $P$ is regular, it is known $H^{1}(G, k)\simeq H^{1}(N_{G}(P), k)$ and the group $G$ has the following structure: where $I=P\cap O^{p}(G)=P\cap O^{p}(N_{G}(P))$ .  ... 
doi:10.14492/hokmj/1350912972 fatcat:6ci2fdrlvffqvlhtc2zo7kpf6q

Set-theoretic aspects of periodic FC-groups --- extraspecial p-groups and Kurepa trees [article]

Jörg Brendle
1992 arXiv   pre-print
A group G is FC iff every element g in G has finitely many conjugates. A p-group E is called extraspecial iff Phi (E) = E' = Z(E) cong Z_p, the cyclic group with p elements.  ...  In particular, there is an extraspecial p-group with this property if there is a Kurepa tree.  ...  Extraspecial p-groups and Kurepa trees 5.1. The goal of this section is a detailed investigation of extraspecial p-groups, especially of those of size ω 2 .  ... 
arXiv:math/9211201v1 fatcat:5247ymsr4bamnkxmhpbrpyrm3i

Cayley graphs for extraspecial p-groups and a covering graph perspective on Huang's theorem [article]

Maxwell Levit
2020 arXiv   pre-print
Inspired by Tao's observation, we generalize the Cohen-Tits cover by constructing, as Cayley graphs for extraspecial p-groups, two infinite families of 4-cycle-free p-fold covers of the Cartesian product  ...  of p-cycles.  ...  Fix a prime p. A p-group G is extraspecial if its center Z = Z(G) is a cyclic group of order p and G/Z is a (non-trivial) elementary abelian p-group.  ... 
arXiv:2010.14634v2 fatcat:rvhw5zxi65czpfky5y5t4peg2a

Free Actions of Extraspecial p-Groups on S^n × S^n [article]

Ian Hambleton, Ozgun Unlu
2007 arXiv   pre-print
Let p be an odd regular prime, and let G_p denote the extraspecial p--group of order p^3 and exponent p. We show that G_p acts freely and smoothly on S^2p-1× S^2p-1.  ...  For p=3 we explicitly construct a free smooth action of a Lie group G_3 containing G_3 on S^5× S^5.  ...  The Proof of Theorem C In this section let G denote the group G 3 , which contains the extraspecial 3-group of order 27 and exponent 3.  ... 
arXiv:math/0701558v1 fatcat:l5c5di56drennn3fn7f7ogcqqy

The classification of p-local finite groups over the extraspecial group of order p3 and exponent p

Albert Ruiz, Antonio Viruel
2004 Mathematische Zeitschrift  
In this paper we classify the p-local finite groups over p 1+2 + , the extraspecial group of order p 3 and exponent p for odd p.  ...  This study reduces to the classification of the saturated fusion systems over p 1+2 + , which will be characterized by the outer automorphism group, the number of F-radical subgroups and the automorphism  ...  p > 2, of order p 3 , then S is isomorphic to the extraspecial group of order p 3 and exponent p, denoted by p 1+2 + , and p ≤ 13.  ... 
doi:10.1007/s00209-004-0652-1 fatcat:pxa6edr3jrczfgv5gggx6jykzu

Representations of the Double Burnside Algebra and Cohomology of the Extraspecial p-Group [article]

Akihiko Hida, Nobuaki Yagita
2012 arXiv   pre-print
Let E be the extraspecial p-group of order p^3 and exponent p where p is an odd prime.  ...  We determine the mod p cohomology of summands in the stable splitting of p-completed classifying space BE modulo nilpotence.  ...  Introduction Let p be an odd prime and E = p 1+2 + the extraspecial p-group of order p 3 and exponent p.  ... 
arXiv:1210.0639v1 fatcat:2xvyg4qypfdzbp54un6enn2qse

Representations of the double Burnside algebra and cohomology of the extraspecial p-group II [article]

Akihiko Hida, Nobuaki Yagita
2015 arXiv   pre-print
Let E be the extraspecial p-group of order p^3 and exponent p where p is an odd prime. We consider the mod p cohomology of summands in the stable splitting of p-completed classifying space BE.  ...  Moreover, we consider the stable splitting for some finite groups with Sylow p-subgroup E.  ...  Introduction Let p be an odd prime and E = p 1+2 + the extraspecial p-group of order p 3 and exponent p.  ... 
arXiv:1505.06038v1 fatcat:jk33q2xfwjfflpaghkoox75ga4
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