B. Amberg, L. S. Kazarin, “$ABA$-groups with cyclic subgroup $B$”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 3, 2012, 10

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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2012, Volume 18, Number 3, Pages 10–22 (Mi timm833)

This article is cited in 5 scientific papers (total in 5 papers)

A B A

$ABA$ -groups with cyclic subgroup

B

$B$

B. Amberg^a, L. S. Kazarin^b

^a Johannes Gutenberg-Universität, Mainz
^b Кафедра алгебры и мат. логики, Ярославский гос. университет им. П. Г. Демидова

Full-text PDF (219 kB) Citations (5)

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Abstract: Some criteria to the solubility of groups of the form

G = A B A

$G=ABA$ with a nilpotent subgroup

A

$A$ and a cyclic subgroup

B

$B$ are derived. In particular, it is proved (using the classification of the finite simple groups) that the finite group

G = A B A

$G=ABA$ is soluble if

A

$A$ is a nilpotent group of odd order and

B

$B$ is a cyclic group and

(| A |, | B |) = 1

$(|A|,|B|)=1$ .

Keywords: simple group, Lie type group, sporadic simple group.

Received: 30.01.2012

Bibliographic databases:

Document Type: Article

UDC: 512.54

Language: English

Citation: B. Amberg, L. S. Kazarin, “

A B A

$ABA$ -groups with cyclic subgroup

B

$B$ ”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 3, 2012, 10–22

Citation in format AMSBIB

\Bibitem{AmbKaz12}

\by B.~Amberg, L.~S.~Kazarin

\paper $ABA$-groups with cyclic subgroup~$B$

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

\yr 2012

\vol 18

\issue 3

\pages 10--22

\mathnet{http://mi.mathnet.ru/timm833}

\elib{https://elibrary.ru/item.asp?id=17937004}

Linking options:

https://www.mathnet.ru/eng/timm833

https://www.mathnet.ru/eng/timm/v18/i3/p10

This publication is cited in the following 5 articles:

Kazarin L., “Factorizations of Finite Groups and Related Topics”, Algebr. Colloq., 27:1, SI (2020), 149–180
L. S. Kazarin, S. S. Poiseeva, “On Finite Groups With Large Degrees of Irreducible Character”, Autom. Control Comp. Sci., 50:7 (2016), 497–509
L. S. Kazarin, I. A. Rassadin, D. N. Sakharov, “O suschestvovanii ABA-faktorizatsii u sporadicheskikh grupp ranga 3”, Model. i analiz inform. sistem, 22:2 (2015), 219–237
L. S. Kazarin, S. S. Poiseeva, “Finite Groups with Large Irreducible Character”, Math. Notes, 98:2 (2015), 265–272
L. S. Kazarin, S. S. Poiseeva, “O konechnykh gruppakh s bolshoi stepenyu neprivodimogo kharaktera”, Model. i analiz inform. sistem, 22:4 (2015), 483–499

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

Trudy Instituta Matematiki i Mekhaniki UrO RAN

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References:	76
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