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- W4387390081 abstract "We continue the analysis of the Modular Isomorphism Problem for $2$-generated $p$-groups with cyclic derived subgroup, $p>2$, started in [D. Garc'ia-Lucas, 'A. del R'io, and M. Stanojkovski. On group invariants determined by modular group algebras: even versus odd characteristic. Algebr. Represent. Theory. https://doi.org/10.1007/s10468-022-10182-x, 2022]. We show that if $G$ belongs to this class of groups, then the isomorphism type of the quotients $G/(G')^{p^3}$ and $G/gamma_3(G)^p$ are determined by its modular group algebra. In fact, we obtain a more general but technical result, expressed in terms of the classification cite{OsnelDiegoAngel}. We also show that for groups in this class of order at most $p^{11}$, the Modular Isomorphism Problem has positive answer. Finally, we describe some families of groups of order $p^{12}$ whose group algebras over the field with $p$ elements cannot be distinguished with the techniques available to us." @default.
- W4387390081 created "2023-10-06" @default.
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- W4387390081 date "2023-10-04" @default.
- W4387390081 modified "2023-10-07" @default.
- W4387390081 title "On the Modular Isomorphism Problem for 2-generated groups with cyclic derived subgroup" @default.
- W4387390081 doi "https://doi.org/10.48550/arxiv.2310.02627" @default.
- W4387390081 hasPublicationYear "2023" @default.
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