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Journal articles on the topic 'Pro-p groups'

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Published: 9 March 2023
Last updated: 10 March 2023

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1

Quadrelli, Claudio. "$1$-smooth pro-$p$ groups and Bloch–Kato pro-$p$ groups." Homology, Homotopy and Applications 24, no. 2 (2022): 53–67. http://dx.doi.org/10.4310/hha.2022.v24.n2.a3.

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2

Mel'nikov, O. V. "Aspherical pro-$ p$-groups." Sbornik: Mathematics 193, no. 11 (December 31, 2002): 1639–70. http://dx.doi.org/10.1070/sm2002v193n11abeh000692.

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3

Salehi Golsefidy, Alireza. "Character degrees of p-groups and pro-p groups." Journal of Algebra 286, no. 2 (April 2005): 476–91. http://dx.doi.org/10.1016/j.jalgebra.2004.12.013.

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4

Herfort, Wolfgang, and Pavel Zalesskii. "Virtually free pro-p groups." Publications mathématiques de l'IHÉS 118, no. 1 (February 16, 2013): 193–211. http://dx.doi.org/10.1007/s10240-013-0051-4.

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5

Mattarei, Sandro. "Some Thin Pro-p-Groups." Journal of Algebra 220, no. 1 (October 1999): 56–72. http://dx.doi.org/10.1006/jabr.1998.7809.

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6

Afanas’eva, S. G., and N. S. Romanovskii. "Rigid Metabelian Pro-p-Groups." Algebra and Logic 53, no. 2 (May 2014): 102–13. http://dx.doi.org/10.1007/s10469-014-9274-9.

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7

Gavioli, Norberto, Valerio Monti, and Carlo Maria Scoppola. "Pro-p groups with waists." Journal of Algebra 351, no. 1 (February 2012): 130–37. http://dx.doi.org/10.1016/j.jalgebra.2011.11.022.

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8

Morishita, Masanori, and Yuji Terashima. "p -Johnson homomorphisms and pro- p groups." Journal of Algebra 479 (June 2017): 102–36. http://dx.doi.org/10.1016/j.jalgebra.2017.01.028.

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9

Herfort, Wolfgang, Pavel Zalesskii, and Theo Zapata. "Splitting theorems for pro-p groups acting on pro-p trees." Selecta Mathematica 22, no. 3 (January 8, 2016): 1245–68. http://dx.doi.org/10.1007/s00029-015-0217-7.

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10

Andozhskiĭ, I. V., and V. M. Tsvetkov. "ANALYTIC PRO-p-GROUPS OF RANK 3 AND CLOSED PRO-p-GROUPS OF TYPE (3,4)." Mathematics of the USSR-Izvestiya 27, no. 3 (June 30, 1986): 593–99. http://dx.doi.org/10.1070/im1986v027n03abeh001202.

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11

Sonn, Jack. "Free pro-p groups as galois groups over ℚ(p)(t)." Israel Journal of Mathematics 119, no. 1 (December 2000): 1–8. http://dx.doi.org/10.1007/bf02810660.

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12

Afanaseva, S. G., and E. I. Timoshenko. "Partially commutative metabelian pro-$p$-groups." Sibirskii matematicheskii zhurnal 60, no. 4 (June 30, 2019): 717–23. http://dx.doi.org/10.33048/smzh.2019.60.401.

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13

Hillman, Jonathan A., and Alexander Schmidt. "Pro-p groups of positive deficiency." Bulletin of the London Mathematical Society 40, no. 6 (October 3, 2008): 1065–69. http://dx.doi.org/10.1112/blms/bdn089.

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14

Leedham-Green, C. R. "Pro-p -Groups of Finite Coclass." Journal of the London Mathematical Society 50, no. 1 (August 1994): 43–48. http://dx.doi.org/10.1112/jlms/50.1.43.

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15

Afanaseva, S. G., and E. I. Timoshenko. "Partially Commutative Metabelian Pro-P-Groups." Siberian Mathematical Journal 60, no. 4 (July 2019): 559–64. http://dx.doi.org/10.1134/s0037446619040013.

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16

Shalev, A., and E. I. Zelmanov. "Pro-p groups of finite coclass." Mathematical Proceedings of the Cambridge Philosophical Society 111, no. 3 (May 1992): 417–21. http://dx.doi.org/10.1017/s0305004100075514.

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In 1980 Leedham-Green and Newman made a series of conjectures on the structure of pro-p groups and finite p-groups of a given coclass [10]. These insightful conjectures have gradually been proved, in a series of papers (some of which are still unpublished) by Leedham-Green, Donkin, McKay and Plesken (see, e.g. [11, 2, 8, 9, 13, 14]). Some simplifications (as well as additional information) have recently been given in [12, 15].
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17

KOCHLOUKOVA, DESSISLAVA H., and PAVEL A. ZALESSKII. "Subdirect products of pro-p groups." Mathematical Proceedings of the Cambridge Philosophical Society 158, no. 2 (January 9, 2015): 289–303. http://dx.doi.org/10.1017/s030500411400067x.

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AbstractWe study when a pro-p subdirect product S ⩽ G1 × . . . × Gn is of type FPm for m ⩾ 2 for some special pro-p groups Gi. In particular we treat the case when Gi is a finitely generated non-trivial free pro-p product different from C2 ∐ C2 if p = 2 or a non-abelian pro-p group from the class $\mathcal{L}$ defined in [12].
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18

KING, JEREMY D. "Embedding theorems for pro-p groups." Mathematical Proceedings of the Cambridge Philosophical Society 123, no. 2 (March 1998): 217–26. http://dx.doi.org/10.1017/s0305004197002181.

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19

Wilkes, Gareth. "On accessibility for pro-p groups." Journal of Algebra 525 (May 2019): 1–18. http://dx.doi.org/10.1016/j.jalgebra.2019.01.022.

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20

Baumann, B. "Free pro-p groups with operators." Manuscripta Mathematica 73, no. 1 (December 1991): 385–96. http://dx.doi.org/10.1007/bf02567649.

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21

Zubkov, A. N. "Varieties of metabelian pro-p-groups." Siberian Mathematical Journal 33, no. 5 (1992): 816–25. http://dx.doi.org/10.1007/bf00970989.

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22

Fernández-Alcober, Gustavo A., Jon González-Sánchez, and Andrei Jaikin-Zapirain. "Omega subgroups of pro-p groups." Israel Journal of Mathematics 166, no. 1 (August 2008): 393–412. http://dx.doi.org/10.1007/s11856-008-1036-8.

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23

Efrat, Ido. "Small maximal pro-p Galois groups." Manuscripta Mathematica 95, no. 1 (December 1998): 237–49. http://dx.doi.org/10.1007/bf02678028.

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24

Kochloukova, D. H., and P. A. Zalesskii. "Fully residually free pro-p groups." Journal of Algebra 324, no. 4 (August 2010): 782–92. http://dx.doi.org/10.1016/j.jalgebra.2010.04.019.

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25

Kochloukova, Dessislava H., and Pavel Zalesskii. "Free-by-Demushkin pro-p groups." Mathematische Zeitschrift 249, no. 4 (October 15, 2004): 731–39. http://dx.doi.org/10.1007/s00209-004-0720-6.

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26

Efrat, Ido. "Small maximal pro-p Galois groups." manuscripta mathematica 95, no. 2 (February 1998): 237–49. http://dx.doi.org/10.1007/s002290050026.

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27

Pinto, Aline G. S. "Homological finiteness properties of pro-p modules over metabelian pro-p groups." Journal of Algebra 301, no. 1 (July 2006): 96–111. http://dx.doi.org/10.1016/j.jalgebra.2005.09.002.

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28

Wilson, John S. "Finite presentations of pro-p groups and discrete groups." Inventiones Mathematicae 105, no. 1 (December 1991): 177–83. http://dx.doi.org/10.1007/bf01232262.

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29

Wilson, Lawrence E. "Torsion elements in p-adic analytic pro-p groups." Journal of Algebra 277, no. 2 (July 2004): 806–24. http://dx.doi.org/10.1016/s0021-8693(03)00534-9.

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30

SALLE, LANDRY. "MILD PRO-p-GROUPS AS GALOIS GROUPS OVER GLOBAL FIELDS." International Journal of Number Theory 05, no. 05 (August 2009): 779–95. http://dx.doi.org/10.1142/s1793042109002377.

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This paper is devoted to finding new examples of mild pro-p-groups as Galois groups over global fields, following the work of Labute ([6]). We focus on the Galois group [Formula: see text] of the maximal T-split S-ramified pro-p-extension of a global field k. We first retrieve some facts on presentations of such a group, including a study of the local-global principle for the cohomology group [Formula: see text], then we show separately in the case of function fields and in the case of number fields how it can be used to find some mild pro-p-groups.
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31

Kochloukova, Dessislava H., and Pavel Zalesskii. "Homological Invariants for pro-p Groups and Some Finitely Presented pro- ${\cal C}$ Groups." Monatshefte f�r Mathematik 144, no. 4 (March 23, 2005): 285–96. http://dx.doi.org/10.1007/s00605-004-0269-9.

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32

Würfel, Tilmann. "Dimension-Preserving Extensions of Pro-p-Groups." Canadian Mathematical Bulletin 34, no. 1 (March 1, 1991): 136–40. http://dx.doi.org/10.4153/cmb-1991-022-3.

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AbstractWe investigate extensions of pro-p-groups 1 —> N —> G —> Γ —> 1 where N is pro-p-free and Nab, is a free Zp[Γ]-module. In case Γ is finite we show that such an extension splits modulo the second derived group N".
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33

Jaikin-Zapirain, Andrei, and Benjamin Klopsch. "Analytic groups over general pro-p domains." Journal of the London Mathematical Society 76, no. 2 (October 2007): 365–83. http://dx.doi.org/10.1112/jlms/jdm055.

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34

Engler, Antonio José, and Jochen Koenigsmann. "Abelian subgroups of pro-$p$ Galois groups." Transactions of the American Mathematical Society 350, no. 6 (1998): 2473–85. http://dx.doi.org/10.1090/s0002-9947-98-02063-7.

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35

Barnea, Yiftach, and Robert Guralnick. "Subgroup growth in some pro-$p$ groups." Proceedings of the American Mathematical Society 130, no. 3 (August 29, 2001): 653–59. http://dx.doi.org/10.1090/s0002-9939-01-06099-3.

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36

BARNEA, YIFTACH. "RESIDUAL PROPERTIES OF FREE PRO-P GROUPS." Bulletin of the London Mathematical Society 33, no. 5 (September 2001): 578–82. http://dx.doi.org/10.1112/s0024609301008281.

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Recall that if S is a class of groups, then a group G is residually-S if, for any element 1 ≠ g ∈ G, there is a normal subgroup N of G such that g ∉ N and G/N ∈ S. Let Λ be a commutative Noetherian local pro-p ring, with a maximal ideal M. Recall that the first congruence subgroup of SLd(Λ) is: SL1d(Λ) = ker (SLd(Λ) → SLd(Λ/M)).Let K ⊆ ℕ. We define SΛ(K) = ∪d∈K{open subgroups of SL1d(Λ)}. We show that if K is infinite, then for Λ = [ ]p[[t]] and for Λ = ℤp a finitely generated non-abelian free pro-p group is residually-SΛ(K). We apply a probabilistic method, combined with Lie methods and a result on random generation in simple algebraic groups over local fields. It is surprising that the case of zero characteristic is deduced from the positive characteristic case.
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37

Jaikin-Zapirain, Andrei. "On linear just infinite pro-p groups." Journal of Algebra 255, no. 2 (September 2002): 392–404. http://dx.doi.org/10.1016/s0021-8693(02)00024-8.

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38

Koenigsmann, Jochen. "Pro-p galois groups of rank ≤4." Manuscripta Mathematica 95, no. 1 (December 1998): 251–71. http://dx.doi.org/10.1007/bf02678029.

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39

Hillman, Jonathan, Dessislava Kochloukova, and Igor Lima. "Pro-p completions of Poincaré duality groups." Israel Journal of Mathematics 200, no. 1 (June 2014): 1–17. http://dx.doi.org/10.1007/s11856-013-0074-z.

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40

Klopsch, B., and I. Snopce. "A CHARACTERIZATION OF UNIFORM PRO-p GROUPS." Quarterly Journal of Mathematics 65, no. 4 (March 11, 2014): 1277–91. http://dx.doi.org/10.1093/qmath/hau005.

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41

Herfort, W., and P. A. Zalesskii. "Cyclic Extensions of Free Pro-p Groups." Journal of Algebra 216, no. 2 (June 1999): 511–47. http://dx.doi.org/10.1006/jabr.1998.7787.

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42

Lubotzky, Alexander, and Aner Shalev. "On some Λ-analytic pro-p groups." Israel Journal of Mathematics 85, no. 1-3 (February 1994): 307–37. http://dx.doi.org/10.1007/bf02758646.

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43

Bush, Michael R., and John Labute. "Mild pro-p-groups with 4 generators." Journal of Algebra 308, no. 2 (February 2007): 828–39. http://dx.doi.org/10.1016/j.jalgebra.2006.08.002.

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44

Barnea, Y., N. Gavioli, A. Jaikin-Zapirain, V. Monti, and C. M. Scoppola. "Pro-p groups with few normal subgroups." Journal of Algebra 321, no. 2 (January 2009): 429–49. http://dx.doi.org/10.1016/j.jalgebra.2008.10.012.

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45

Moravec, Primož. "On pro-p groups with potent filtrations." Journal of Algebra 322, no. 1 (July 2009): 254–58. http://dx.doi.org/10.1016/j.jalgebra.2009.01.011.

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46

MacQuarrie, J. W. "Green correspondence for virtually pro-p groups." Journal of Algebra 323, no. 8 (April 2010): 2203–8. http://dx.doi.org/10.1016/j.jalgebra.2010.02.011.

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47

Ribes, Luis. "Virtually free factors of pro-p groups." Israel Journal of Mathematics 74, no. 2-3 (October 1991): 337–46. http://dx.doi.org/10.1007/bf02775795.

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48

Klopsch, Benjamin. "Pro- p groups with linear subgroup growth." Mathematische Zeitschrift 245, no. 2 (October 1, 2003): 335–70. http://dx.doi.org/10.1007/s00209-003-0548-5.

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49

Koenigsmann, Jochen. "Pro-p Galois groups of rank ≤ 4." manuscripta mathematica 95, no. 2 (February 1998): 251–71. http://dx.doi.org/10.1007/s002290050027.

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50

Roman'kov, V. A. "Infinite generation of automorphism groups of free pro-p groups." Siberian Mathematical Journal 34, no. 4 (1993): 727–32. http://dx.doi.org/10.1007/bf00975176.

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