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Also the degrees sequence of {\\Gamma}(G) is called the degree pattern of G and is denoted by D(G). In this paper, first we classify the finite C{\\theta}{\\theta}-groups with even order. Then we show that there are infinitely many C{\\theta}{\\theta}-groups with the same degree pattern. Finally, we proved that the simple group PSL(2, q) and the almo"},"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":"1703.00635","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-03-02T06:40:08Z","cross_cats_sorted":[],"title_canon_sha256":"9e33f81ede4fc37b7f4b4374ef5e8ab443181ee03a94c13b256b479f0c611c1d","abstract_canon_sha256":"13c54fd489d9a55a82a3fba0db1f26f484f3d7fddd6d76a8de2f0fe61421f4ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:41.192926Z","signature_b64":"2oF125YvXWsFTU0totW0GRDsMYYadXSWWo1AhW/tqRMnDGgYYlwEVktWEZPNjgsv1Htfivoe8f+wYULWqzUhBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe3c716e2db22b39dceabb708726902f42cdb574cc87c12060b7e14307767c5b","last_reissued_at":"2026-05-18T00:49:41.192513Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:41.192513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of finite C{\\theta}{\\theta}-groups with even order and its application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ali Mahmoudifar","submitted_at":"2017-03-02T06:40:08Z","abstract_excerpt":"A finite group of order divisible by 3 in which centralizers of 3-elements are 3-subgroups will be called a C{\\theta}{\\theta}-group. 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