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 -