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Extraspecial p-groups

1987
*
Annals of Pure and Applied Logic
*

It is shown that there is a class of cardinals 3-for which there are 2 x

doi:10.1016/0168-0072(87)90041-8
fatcat:6rzq5hqdujc4dflaf5haa7g2ai
*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. ...##
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Essential cohomology and extraspecial $p$-groups

2000
*
Transactions of the American Mathematical Society
*

Let us recall that an

doi:10.1090/s0002-9947-00-02689-1
fatcat:6iuhcdrgjrbzzfzr2o6zrvoy4a
*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. ...##
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The Dade group of (almost) extraspecial p-groups

2004
*
Journal of Pure and Applied Algebra
*

In this paper, we determine a presentation by explicit generators and relations for the Dade

doi:10.1016/j.jpaa.2004.02.008
fatcat:dtyitwwkqfb5lp6pqq5sb3vgbq
*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 . ...##
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Almost all extraspecial p-groups are swan groups

2000
*
Bulletin of the Australian Mathematical Society
*

Let

doi:10.1017/s0004972700018566
fatcat:dq6zngwenjar5k453hkzgfzxqm
*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*. ...##
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Almost All Generalized Extraspecial p-Groups Are Resistant

2002
*
Journal of Algebra
*

Let

doi:10.1006/jabr.2001.9069
fatcat:ct627phypvhr3h3k252bubqteu
*P*be a generalized*extraspecial**p*-*group*. ... Let*P*be a generalized*extraspecial**p*-*group*. ...##
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Transfer and Chern classes for extraspecial p-groups

2008
*
arXiv
*
pre-print

In the cohomology ring of an

arXiv:0809.2920v1
fatcat:d6m7tu7tzrbbpdz33mnukjrk6e
*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. ...##
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The K(n)-Euler characteristic of extraspecial p-groups

2001
*
Journal of Pure and Applied Algebra
*

Let

doi:10.1016/s0022-4049(99)00102-4
fatcat:uegpqlzkwbb7raiyvayridvmfi
*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 . ...##
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On the Conjugacy Search Problem in Extraspecial p-Groups
[article]

2022
*
arXiv
*
pre-print

This paper demonstrates a polynomial time solution of the CSP in an important class of nonabelian

arXiv:2203.03526v1
fatcat:b2znck2hjnfjtkglf4jikw7ad4
*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 . ...##
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Mod p cohomology algebras of finite groups with extraspecial Sylow p-subgroups

2000
*
Hokkaido Mathematical Journal
*

INTRODUCTION The following

doi:10.14492/hokmj/1350912972
fatcat:6ci2fdrlvffqvlhtc2zo7kpf6q
*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 $I=*P*\cap O^{*p*}(G)=*P*\cap O^{*p*}(N_{G}(*P*))$ . ...##
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Set-theoretic aspects of periodic FC-groups --- extraspecial p-groups and Kurepa trees
[article]

1992
*
arXiv
*
pre-print

A

arXiv:math/9211201v1
fatcat:5247ymsr4bamnkxmhpbrpyrm3i
*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 . ...##
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Cayley graphs for extraspecial p-groups and a covering graph perspective on Huang's theorem
[article]

2020
*
arXiv
*
pre-print

Inspired by Tao's observation, we generalize the Cohen-Tits cover by constructing, as Cayley graphs for

arXiv:2010.14634v2
fatcat:rvhw5zxi65czpfky5y5t4peg2a
*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*. ...##
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Free Actions of Extraspecial p-Groups on S^n × S^n
[article]

2007
*
arXiv
*
pre-print

Let

arXiv:math/0701558v1
fatcat:l5c5di56drennn3fn7f7ogcqqy
*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. ...##
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The classification of p-local finite groups over the extraspecial group of order p3 and exponent p

2004
*
Mathematische Zeitschrift
*

In this paper we classify the

doi:10.1007/s00209-004-0652-1
fatcat:pxa6edr3jrczfgv5gggx6jykzu
*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. ...##
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Representations of the Double Burnside Algebra and Cohomology of the Extraspecial p-Group
[article]

2012
*
arXiv
*
pre-print

Let E be the

arXiv:1210.0639v1
fatcat:2xvyg4qypfdzbp54un6enn2qse
*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*. ...##
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Representations of the double Burnside algebra and cohomology of the extraspecial p-group II
[article]

2015
*
arXiv
*
pre-print

Let E be the

arXiv:1505.06038v1
fatcat:jk33q2xfwjfflpaghkoox75ga4
*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*. ...
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