@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",
}