A. G. Rubashkin, K. A. Filippov, “Periodic groups saturated with the groups $L_2(p^n)$”, Sibirsk. Mat. Zh., 46:6 (2005), 1388–1392; Siberian Math. J., 46:6 (2005), 1119

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Sibirskii Matematicheskii Zhurnal, 2005, Volume 46, Number 6, Pages 1388–1392 (Mi smj1047)

This article is cited in 27 scientific papers (total in 27 papers)

Periodic groups saturated with the groups

L_{2} (p^{n})

$L_2(p^n)$

A. G. Rubashkin, K. A. Filippov

Krasnoyarsk State Agricultural University

Full-text PDF (171 kB) Citations (27)

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Abstract: Given an indexing set

I

$I$ and a finite field

K_{α}

$K_\alpha$ for each

α \in I

$\alpha\in I$ ,

$\mathfrak R=\{L_2(K_\alpha)|\alpha\in I\}$ and

$\mathfrak N=\{SL_2(K_\alpha)|\alpha\in I\}$ . We prove that each periodic group

$G$ saturated with groups in

$\mathfrak R(\mathfrak N)$ is isomorphic to

$L_2(P)$ (respectively

$SL_2(P)$ ) for a suitable locally finite field

$P$ .

Keywords: saturation, periodic group.

Received: 24.04.2005

English version:
Siberian Mathematical Journal, 2005, Volume 46, Issue 6, Pages 1119–1122
DOI: https://doi.org/10.1007/s11202-005-0106-y

Bibliographic databases:

UDC: 512.54

Language: Russian

Citation: A. G. Rubashkin, K. A. Filippov, “Periodic groups saturated with the groups

$L_2(p^n)$ ”, Sibirsk. Mat. Zh., 46:6 (2005), 1388–1392; Siberian Math. J., 46:6 (2005), 1119–1122

Citation in format AMSBIB

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\vol 46

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Linking options:

https://www.mathnet.ru/eng/smj1047

https://www.mathnet.ru/eng/smj/v46/i6/p1388

This publication is cited in the following 27 articles:

A. A. Shlepkin, “Shunkov groups saturated by general linear groups of degree 3”, Siberian Math. J., 63:2 (2022), 374–386
D. V. Lytkina, V. D. Mazurov, “Periodic groups saturated with finite simple symplectic groups of dimension 6 over fields of odd characteristics”, Siberian Math. J., 63:6 (2022), 1117–1120
D. V. Lytkina, V. D. Mazurov, “On characterization of simple orthogonal groups of odd dimension in the class of periodic groups”, Siberian Math. J., 62:1 (2021), 77–83
D. V. Lytkina, V. D. Mazurov, “On the periodic groups saturated with finite simple groups of lie type $b_3$ ”, Siberian Math. J., 61:3 (2020), 499–503
X. Zhu, D. V. Lytkina, V. D. Mazurov, “Characterization of Locally Finite Simple Groups of Type $G_2$ over Fields of Odd Characteristics in the Class of Periodic Groups”, Math. Notes, 105:4 (2019), 513–518
A. A. Shlepkin, “O gruppakh, nasyschennykh gruppami diedra i lineinymi gruppami stepeni $2$ ”, Sib. elektron. matem. izv., 15 (2018), 74–85
D. V. Lytkina, A. A. Shlepkin, “Periodic groups saturated with the linear groups of degree $2$ and the unitary groups of degree $3$ over finite fields of odd characteristic”, Siberian Adv. Math., 28:3 (2018), 175–186
D. V. Lytkina, A. I. Sozutov, A. A. Shlepkin, “Periodicheskie gruppy 2-ranga dva, nasyschennye konechnymi prostymi gruppami”, Sib. elektron. matem. izv., 15 (2018), 786–796
D. V. Lytkina, V. D. Mazurov, “Characterization of simple symplectic groups of degree 4 over locally finite fields in the class of periodic groups”, Algebra and Logic, 57:3 (2018), 201–210
X. Wei, W. Guo, D. V. Lytkina, V. D. Mazurov, “Characterization of locally finite simple groups of the type $^3D_4$ over fields of odd characteristic in the class of periodic groups”, Siberian Math. J., 59:5 (2018), 799–804
Daria V. Lytkina, Victor D. Mazurov, “Characterizations of simple linear groups in the class of periodic groups”, Zhurn. SFU. Ser. Matem. i fiz., 10:3 (2017), 287–292
D. V. Lytkina, V. D. Mazurov, “Characterization of simple symplectic groups of degree $4$ over locally finite fields of characteristic $2$ in the class of periodic groups”, Siberian Math. J., 58:5 (2017), 850–858
A. A. Shlepkin, “Shunkov groups saturated with general linear groups”, Siberian Math. J., 57:1 (2016), 174–184
A. A. Shlepkin, “O periodicheskoi gruppe Shunkova, nasyschennoi konechnymi prostymi gruppami lieva tipa ranga 1”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 16 (2016), 102–116
A. A. Shlepkin, “On the periodic groups saturated with projective linear groups”, Siberian Math. J., 56:4 (2015), 761–764
D. V. Lytkina, V. D. Mazurov, “Periodicheskie gruppy, nasyschennye konechnymi prostymi gruppami”, Tr. In-ta matem., 23:2 (2015), 72–75
A. A. Shlepkin, I. V. Sabodakh, “O gruppe Shunkova, nasyschennoi $GL_2(p^n)$ ”, Sib. elektron. matem. izv., 11 (2014), 734–744
K. A. Filippov, “On periodic groups saturated by finite simple groups”, Siberian Math. J., 53:2 (2012), 345–351
Konstantin A. Filippov, “O gruppakh Shunkova s odnim usloviem nasyschennosti”, Zhurn. SFU. Ser. Matem. i fiz., 5:3 (2012), 430–436
Lytkina D.V., “Periodic groups with given properties of finite subgroups”, Doklady Mathematics, 85:1 (2012), 55–56

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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