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Group extensions and marginal series of pair of groups
Mohammad Reza Rismanchian1
1 Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Iran
Comptes Rendus. Mathématique, Volume 359 (2021) no. 5, pp. 631-638.

In this article, using the concept of generalized Baer-invariant of a pair of groups, we establish some related isomorphisms between lower marginal quotient pairs of groups, which are generalized versions of some isomorphisms of Stallings. We also derive a result for the pair (𝒱.𝒲,𝒳) to be an ultra Hall pair for special varieties of groups. This result generalizes that of Fung in 1977, which has roots in Philip Hall’s criterion on nilpotency.

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DOI : 10.5802/crmath.212
Classification : 20E10, 20F19, 20J05

Mohammad Reza Rismanchian 1

1 Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Iran
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Mohammad Reza Rismanchian. Group extensions and marginal series of pair of groups. Comptes Rendus. Mathématique, Volume 359 (2021) no. 5, pp. 631-638. doi : 10.5802/crmath.212. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.212/

[1] Graham Ellis The schur multiplier of a pair of groups, Appl. Categ. Struct., Volume 6 (1998) no. 3, pp. 355-371 | DOI | MR | Zbl

[2] W. K. H. Fung Some theorems of Hall type, Arch. Math., Volume 27 (1977), pp. 9-20 | DOI | MR | Zbl

[3] Philip Hall The classification of prime power groups, J. Reine Angew. Math., Volume 182 (1940), pp. 130-141 | MR

[4] N. S. Hekster Varities of groups and isologisms, J. Aust. Math. Soc., Volume 46 (1989), pp. 22-60 | DOI | MR | Zbl

[5] Peter J. Hilton; Urs Stammbach A Course in Homological Algebra, Graduate Texts in Mathematics, 4, Springer, 1970 | Zbl

[6] J. A. Hulse; John C. Lennox Marginal series in groups, Proc. R. Soc. Edinb., Sect. A, Math., Volume 76 (1977), pp. 139-154 | DOI | Zbl

[7] C. R. Leedham-Green; Susan McKay Baer-invariant, isologism, varietal laws and homology, Acta Math., Volume 137 (1976), pp. 99-150 | DOI | MR | Zbl

[8] Hanna Neumann Varieties of Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, 37, Springer, 1967 | MR | Zbl

[9] Mohammad Reza Rismanchian 𝒱-nilpotent groups and 5-term exact sequence, Commun. Algebra, Volume 42 (2014) no. 4, pp. 1559-1564 | DOI | MR | Zbl

[10] Mohammad Reza Rismanchian; Mehdi Araskhan Some inequalities for the dimension of the Schur multiplier of a pair of (nilpotent) Lie Algebras, J. Algebra, Volume 352 (2012) no. 1, pp. 173-179 | DOI | MR | Zbl

[11] Mohammad Reza Rismanchian; Mehdi Araskhan Some properties of the c-nilpotent multiplier and c-covers of Lie algebras, Algebra Colloq., Volume 21 (2014) no. 3, pp. 421-426 | DOI | MR | Zbl

[12] Derek J. S. Robinson A Course in the Theory of Groups, Graduate Texts in Mathematics, 80, Springer, 1995 | Zbl

[13] Issai Schur Über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen, J. für Math., Volume 127 (1904), pp. 20-50 | Zbl

[14] Issai Schur Untersuchungen Über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen, J. Reine Angew. Math., Volume 132 (1907), pp. 85-137 | Zbl

[15] John Stallings Homology and central series of groups, J. Algebra, Volume 2 (1965), pp. 170-181 | DOI | MR

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