{"paper":{"title":"K^*(BG) rings for groups $G=G_{38},...,G_{41}$ of order 32","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Malkhaz Bakuradze, Mamuka Jibladze","submitted_at":"2011-02-16T17:02:15Z","abstract_excerpt":"B. Schuster \\cite{SCH1} proved that the $mod$ 2 Morava $K$-theory $K(s)^*(BG)$ is evenly generated for all groups $G$ of order 32. For the four groups $G$ with the numbers 38, 39, 40 and 41 in the Hall-Senior list \\cite{H}, the ring $K(2)^*(BG)$ has been shown to be generated as a $K(2)^*$-module by transferred Euler classes. In this paper, we show this for arbitrary $s$ and compute the ring structure of $K(s)^*(BG)$. Namely, we show that $K(s)^*(BG)$ is the quotient of a polynomial ring in 6 variables over $K(s)^*(pt)$ by an ideal for which we list explicit generators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3378","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}