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Compatible Actions and Non-abelian Tensor Products. / Bardakov, Valeriy G.; Neshchadim, Mikhail V.

Indian Statistical Institute Series. Springer Science and Business Media B.V., 2018. p. 29-39 (Indian Statistical Institute Series).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

Harvard

Bardakov, VG & Neshchadim, MV 2018, Compatible Actions and Non-abelian Tensor Products. in Indian Statistical Institute Series. Indian Statistical Institute Series, Springer Science and Business Media B.V., pp. 29-39. https://doi.org/10.1007/978-981-13-2047-7_2

APA

Bardakov, V. G., & Neshchadim, M. V. (2018). Compatible Actions and Non-abelian Tensor Products. In Indian Statistical Institute Series (pp. 29-39). (Indian Statistical Institute Series). Springer Science and Business Media B.V.. https://doi.org/10.1007/978-981-13-2047-7_2

Vancouver

Bardakov VG, Neshchadim MV. Compatible Actions and Non-abelian Tensor Products. In Indian Statistical Institute Series. Springer Science and Business Media B.V. 2018. p. 29-39. (Indian Statistical Institute Series). doi: 10.1007/978-981-13-2047-7_2

Author

Bardakov, Valeriy G. ; Neshchadim, Mikhail V. / Compatible Actions and Non-abelian Tensor Products. Indian Statistical Institute Series. Springer Science and Business Media B.V., 2018. pp. 29-39 (Indian Statistical Institute Series).

BibTeX

@inbook{1ab968b2b9984b2ca3f653618c5d5e7a,
title = "Compatible Actions and Non-abelian Tensor Products",
abstract = "For a pair of groups G, H, we study pairs of actions G on H and H on G such that these pairs are compatible. We prove that there are nilpotent group G and some group H such that for G⊗ H the derivative group [G, H] is equal to G. Also, we prove that if Z2 act by inversion on an abelian group A, then the non-abelian tensor product A⊗ Z2 is isomorphic to A.",
keywords = "Compatible action, Nilpotent group, Tensor product",
author = "Bardakov, {Valeriy G.} and Neshchadim, {Mikhail V.}",
note = "Funding Information: The authors gratefully acknowledge the support from the RFBR-16-01-00414 and RFBR-18-01-00057. Also, we thank S. Ivanov and V. Thomas for the interesting discussions and useful suggestions. Publisher Copyright: {\textcopyright} 2018, Springer Nature Singapore Pte Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2018",
doi = "10.1007/978-981-13-2047-7_2",
language = "English",
series = "Indian Statistical Institute Series",
publisher = "Springer Science and Business Media B.V.",
pages = "29--39",
booktitle = "Indian Statistical Institute Series",

}

RIS

TY - CHAP

T1 - Compatible Actions and Non-abelian Tensor Products

AU - Bardakov, Valeriy G.

AU - Neshchadim, Mikhail V.

N1 - Funding Information: The authors gratefully acknowledge the support from the RFBR-16-01-00414 and RFBR-18-01-00057. Also, we thank S. Ivanov and V. Thomas for the interesting discussions and useful suggestions. Publisher Copyright: © 2018, Springer Nature Singapore Pte Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2018

Y1 - 2018

N2 - For a pair of groups G, H, we study pairs of actions G on H and H on G such that these pairs are compatible. We prove that there are nilpotent group G and some group H such that for G⊗ H the derivative group [G, H] is equal to G. Also, we prove that if Z2 act by inversion on an abelian group A, then the non-abelian tensor product A⊗ Z2 is isomorphic to A.

AB - For a pair of groups G, H, we study pairs of actions G on H and H on G such that these pairs are compatible. We prove that there are nilpotent group G and some group H such that for G⊗ H the derivative group [G, H] is equal to G. Also, we prove that if Z2 act by inversion on an abelian group A, then the non-abelian tensor product A⊗ Z2 is isomorphic to A.

KW - Compatible action

KW - Nilpotent group

KW - Tensor product

UR - http://www.scopus.com/inward/record.url?scp=85101600104&partnerID=8YFLogxK

U2 - 10.1007/978-981-13-2047-7_2

DO - 10.1007/978-981-13-2047-7_2

M3 - Chapter

AN - SCOPUS:85101600104

T3 - Indian Statistical Institute Series

SP - 29

EP - 39

BT - Indian Statistical Institute Series

PB - Springer Science and Business Media B.V.

ER -

ID: 28012608