E. P. Vdovin, N. Ch. Manzaeva, D. O. Revin, “On the heritability of the property $D_\pi$ by subgroups”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 4, 2011, 44–52; Proc. Steklov Inst. Math. (Suppl.), 279, suppl. 1 (2012), 130

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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2011, Volume 17, Number 4, Pages 44–52 (Mi timm748)

This article is cited in 10 scientific papers (total in 10 papers)

On the heritability of the property

D_{π}

$D_\pi$ by subgroups

E. P. Vdovin^a, N. Ch. Manzaeva^b, D. O. Revin^a

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Novosibirsk State University

Full-text PDF (181 kB) Citations (10)

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Abstract: For some set of primes

π

$\pi$ , a subgroup

H

$H$ of a finite group

G

$G$ is called a

π

$\pi$ -Hall subgroup if all prime divisors of

| H |

$|H|$ are in

π

$\pi$ and

| G : H |

$|G:H|$ has no prime divisors from

π

$\pi$ . A group

G

$G$ is said to possess the property

D_{π}

$D_\pi$ if it has only one class of conjugate maximal

π

$\pi$ -subgroups or, equivalently, the complete analog of Sylow's theorem for Hall

π

$\pi$ -subgroups is valid in

G

$G$ . We investigate which subgroups of

D_{π}

$D_\pi$ -groups inherit the property

D_{π}

$D_\pi$ .

Keywords: Hall subgroup, property

D_{π}

$D_\pi$ , finite simple group, Sylow's theorem.

Received: 03.06.2011

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2012, Volume 279, Issue 1, Pages 130–138
DOI: https://doi.org/10.1134/S0081543812090106

Bibliographic databases:

Document Type: Article

UDC: 512.542.5

Language: Russian

Citation: E. P. Vdovin, N. Ch. Manzaeva, D. O. Revin, “On the heritability of the property

D_{π}

$D_\pi$ by subgroups”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 4, 2011, 44–52; Proc. Steklov Inst. Math. (Suppl.), 279, suppl. 1 (2012), 130–138

Citation in format AMSBIB

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\paper On the heritability of the property $D_\pi$ by subgroups

\serial Trudy Inst. Mat. i Mekh. UrO RAN

\yr 2011

\vol 17

\issue 4

\pages 44--52

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\elib{https://elibrary.ru/item.asp?id=17870421}

\transl

\jour Proc. Steklov Inst. Math. (Suppl.)

\yr 2012

\vol 279

\issue , suppl. 1

\pages 130--138

\crossref{https://doi.org/10.1134/S0081543812090106}

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Linking options:

https://www.mathnet.ru/eng/timm748

https://www.mathnet.ru/eng/timm/v17/i4/p44

This publication is cited in the following 10 articles:

D. O. Revin, V. D. Shepelev, “The Strong $\pi$ -Sylow Theorem for the Groups PSL ${}_{2}(q)$ ”, Sib Math J, 65:5 (2024), 1187
D. O. Revin, V. D. Shepelev, “Silnaya $\pi$ -teorema Silova dlya grupp PSL $_2(q)$ ”, Sib. matem. zhurn., 65:5 (2024), 1011–1021
Wenbin Guo, Danila O. Revin, Evgeny P. Vdovin, “The reduction theorem for relatively maximal subgroups”, Bull. Math. Sci., 12:01 (2022)
E. P. Vdovin, N. Ch. Manzaeva, D. O. Revin, “On the heritability of the Sylow $\pi$ -theorem by subgroups”, Sb. Math., 211:3 (2020), 309–335
W. Guo, D. O. Revin, “Maximal and submaximal $\mathfrak X$ -subgroups”, Algebra and Logic, 57:1 (2018), 9–28
Wenbin Guo, Danila O. Revin, “Pronormality and Submaximal $\mathfrak {X}$ X -Subgroups on Finite Groups”, Commun. Math. Stat., 6:3 (2018), 289
N. Ch. Manzaeva, “Heritability of the property $\mathcal D_\pi$ by overgroups of $\pi$ -Hall subgroups in the case where $2\in\pi$ ”, Algebra and Logic, 53:1 (2014), 17–28
W. Guo, D. O. Revin, “On the class of groups with pronormal Hall $\pi$ -subgroups”, Siberian Math. J., 55:3 (2014), 415–427
E. P. Vdovin, D. O. Revin, “On the pronormality of Hall subgroups”, Siberian Math. J., 54:1 (2013), 22–28
N. Ch. Manzaeva, “Reshenie problemy Vilanda dlya sporadicheskikh grupp”, Sib. elektron. matem. izv., 9 (2012), 294–305

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

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