Computing a spectral sequence of finite Heisenberg groups of prime power order

2022/02/21 by Ocaña, Oihana Garaialde, Sánchez, Lander Guerrero
#13A02 #18G40 #20D15 #20J06 #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2202.10120

Abstract

Let p≥ 5 be a prime number, let n≥ 2 be a natural number and let Heis(pⁿ) denote the Heisenberg group modulo pⁿ. We study the Lyndon-Hochschild-Serre spectral sequence E(Heis(pⁿ)) associated to Heis(pⁿ) considered as a split extension, and show that, E(Heis(pⁿ)) collapses in the third page. Moreover, for a fixed p, the spectral sequences E(Heis(pⁿ)) are isomorphic from the second page on.

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