{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,12]],"date-time":"2025-06-12T08:10:04Z","timestamp":1749715804739,"version":"3.41.0"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"name":"Prime Minister's Research Fellowship from the Ministry of Education, Government of India","award":["PMRF ID: 0601097"],"award-info":[{"award-number":["PMRF ID: 0601097"]}]},{"name":"DST-FIST","award":["SR\/FST\/MS-I\/2019\/46"],"award-info":[{"award-number":["SR\/FST\/MS-I\/2019\/46"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:p> In 2014, Lubotzky showed that in a finite simple group G every automorphism invariant subset containing the identity is the image of a word map on G. We show that the number of such subsets in a finite nilpotent group may be arbitrarily larger than the number of word images. We construct a 2-exhaustive set of word maps on nilpotent groups of class 2 and demonstrate its minimality in some cases. We also find a sufficient condition, in terms of restrictions on word images, for a group to be a special p-group. <\/jats:p>","DOI":"10.1142\/s0218196725500171","type":"journal-article","created":{"date-parts":[[2025,5,2]],"date-time":"2025-05-02T11:48:18Z","timestamp":1746186498000},"page":"567-585","source":"Crossref","is-referenced-by-count":0,"title":["Word images and their impostors in finite nilpotent groups"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2292-3300","authenticated-orcid":false,"given":"Dilpreet","family":"Kaur","sequence":"first","affiliation":[{"name":"Indian Institute of Technology Jodhpur, Karwar, Rajasthan 342037, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-7852-533X","authenticated-orcid":false,"given":"Harish","family":"Kishnani","sequence":"additional","affiliation":[{"name":"Indian Institute of Science Education and Research Mohali, Sector 81, Mohali 140306, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7687-4183","authenticated-orcid":false,"given":"Amit","family":"Kulshrestha","sequence":"additional","affiliation":[{"name":"Indian Institute of Science Education and Research Mohali, Sector 81, Mohali 140306, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,5,24]]},"reference":[{"key":"S0218196725500171BIB001","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2017.1327065"},{"key":"S0218196725500171BIB002","doi-asserted-by":"publisher","DOI":"10.1090\/coll\/056"},{"key":"S0218196725500171BIB004","volume-title":"Finite Groups","author":"Gorenstein D.","year":"1980","edition":"2"},{"key":"S0218196725500171BIB005","series-title":"Graduate Studies in Mathematics","volume-title":"Classical Groups and Geometric Algebra","volume":"39","author":"Grove L. C.","year":"2002"},{"key":"S0218196725500171BIB006","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.2000.8357"},{"issue":"3","key":"S0218196725500171BIB007","first-page":"27","volume":"88","author":"Kaur D.","year":"2019","journal-title":"Math. Student"},{"key":"S0218196725500171BIB008","doi-asserted-by":"publisher","DOI":"10.1017\/S0017089513000396"},{"key":"S0218196725500171BIB009","doi-asserted-by":"publisher","DOI":"10.1216\/RMJ-1972-2-2-159"},{"key":"S0218196725500171BIB010","doi-asserted-by":"publisher","DOI":"10.1080\/00927871003591900"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196725500171","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,12]],"date-time":"2025-06-12T07:50:21Z","timestamp":1749714621000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196725500171"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,24]]},"references-count":9,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["10.1142\/S0218196725500171"],"URL":"https:\/\/doi.org\/10.1142\/s0218196725500171","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"type":"print","value":"0218-1967"},{"type":"electronic","value":"1793-6500"}],"subject":[],"published":{"date-parts":[[2025,5,24]]}}}