{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T09:50:49Z","timestamp":1747907449471},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","funder":[{"name":"UAEU","award":["G00002968"],"award-info":[{"award-number":["G00002968"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2022,11]]},"abstract":"<jats:p> Let [Formula: see text] be the group algebra of a finite [Formula: see text]-group [Formula: see text] over a finite field [Formula: see text] of positive characteristic [Formula: see text]. Let \u229b be an involution of the algebra [Formula: see text] which is a linear extension of an anti-automorphism of the group [Formula: see text] to [Formula: see text]. If [Formula: see text] is an odd prime, then the order of the \u229b-unitary subgroup of [Formula: see text] is established. For the case [Formula: see text] we generalize a result obtained for finite abelian [Formula: see text]-groups. It is proved that the order of the \u2217-unitary subgroup of [Formula: see text] of a non-abelian [Formula: see text]-group is always divisible by a number which depends only on the size of [Formula: see text], the order of [Formula: see text] and the number of elements of order two in [Formula: see text]. Moreover, we show that the order of the \u2217-unitary subgroup of [Formula: see text] determines the order of the finite [Formula: see text]-group [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196722500576","type":"journal-article","created":{"date-parts":[[2022,7,1]],"date-time":"2022-07-01T05:52:56Z","timestamp":1656654776000},"page":"1327-1334","source":"Crossref","is-referenced-by-count":1,"title":["The order of the unitary subgroups of group algebras"],"prefix":"10.1142","volume":"32","author":[{"given":"Zsolt Adam","family":"Balogh","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, United Arab Emirates University, Al Ain, United Arab Emirates, 15551, United Arab Emirates"}]}],"member":"219","published-online":{"date-parts":[[2022,7,22]]},"reference":[{"key":"S0218196722500576BIB001","doi-asserted-by":"crossref","first-page":"187","DOI":"10.24330\/ieja.852199","volume":"29","author":"Balogh Z.","year":"2021","journal-title":"Int. Electron. 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