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If, in addition, $\\chi$ vanishes at all elements of order divisible by $p$, $\\chi$ is said to be Steinberg-like. For every finite simple group $G$ we determine all primes $p$ for which $G$ admits a Steinberg-like character, except for alternating groups in characteristic~2. Moreover, we determine all primes for which $G$ has a projective $FG$-module of dimension $|S"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.08401","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-22T11:39:47Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"cdc8172e4854c6b559da819ce75f3e89a6a7a405a0ebae9e110e7e12ff88685d","abstract_canon_sha256":"a23633eaedfc5b405e51fa4b81489211af13fded5363dc88f4f43a60c0262424"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:50.803746Z","signature_b64":"B8wiVJZtkckiMC3Jb6Pnz+nnrIRhEZWpHO2KD11IpsFjE96+YOKK5JpelAyDTb5r8/y/bS5f23UCIQw8wYcvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63fa32477a6136365fe058a56dc9ac9257131c5f871db73fe17c6c2fb983909b","last_reissued_at":"2026-05-18T00:25:50.803209Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:50.803209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Steinberg-like characters for finite simple groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Alexandre Zalesski, Gunter Malle","submitted_at":"2017-12-22T11:39:47Z","abstract_excerpt":"Let $G$ be a finite group and, for a prime $p$, let $S$ be a Sylow $p$-subgroup of $G$. 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