{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,15]],"date-time":"2026-08-15T13:21:11Z","timestamp":1786800071929,"version":"3.56.0"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2019,2]]},"abstract":"<jats:p>Recent studies of [Formula: see text]-groups of coclass [Formula: see text] concentrate on the coclass graph [Formula: see text]. While the detailed structure of [Formula: see text] is unknown, it is known that its general structure is dominated by the subgraph of \u2018skeleton groups\u2019. The original definition of these groups is technical, but some modifications for special cases have been used successfully in the literature. Given their importance, in this paper we define and investigate skeleton groups more rigorously. In particular, we study their isomorphism problem, which is a crucial step towards understanding the skeleton subgraph of [Formula: see text]. During our work we identified erroneous arguments for constructing isomorphisms in a proof of the 2013 paper on [Formula: see text]. We correct these errors here by proving the required results in a more general context.<\/jats:p>","DOI":"10.1142\/s0218196718500650","type":"journal-article","created":{"date-parts":[[2018,9,17]],"date-time":"2018-09-17T02:00:36Z","timestamp":1537149636000},"page":"127-146","source":"Crossref","is-referenced-by-count":4,"title":["A note on skeleton groups in coclass graphs"],"prefix":"10.1142","volume":"29","author":[{"given":"Heiko","family":"Dietrich","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Monash University, 1 Wellington Rd, 3800 Clayton, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Subhrajyoti","family":"Saha","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Monash University, 1 Wellington Rd, 3800 Clayton, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2019,2,27]]},"reference":[{"key":"S0218196718500650BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s00013-006-1899-z"},{"key":"S0218196718500650BIB002","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511542756"},{"key":"S0218196718500650BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2014.06.037"},{"key":"S0218196718500650BIB004","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/bdq066"},{"key":"S0218196718500650BIB005","doi-asserted-by":"publisher","DOI":"10.1515\/jgth-2016-0036"},{"key":"S0218196718500650BIB006","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/470\/09185"},{"key":"S0218196718500650BIB007","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511470882"},{"key":"S0218196718500650BIB008","volume-title":"Abstract Algebra","author":"Dummit D. 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