{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T10:17:19Z","timestamp":1695809839699},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2020,8]]},"abstract":"<jats:p>Let [Formula: see text] be a finite solvable group and [Formula: see text] be a subgroup of [Formula: see text]. Suppose that there exists an [Formula: see text]-invariant Carter subgroup [Formula: see text] of [Formula: see text] such that the semidirect product [Formula: see text] is a Frobenius group with kernel [Formula: see text] and complement [Formula: see text]. We prove that the terms of the Fitting series of [Formula: see text] are obtained as the intersection of [Formula: see text] with the corresponding terms of the Fitting series of [Formula: see text], and the Fitting height of [Formula: see text] may exceed the Fitting height of [Formula: see text] by at most one. As a corollary it is shown that for any set of primes [Formula: see text], the terms of the [Formula: see text]-series of [Formula: see text] are obtained as the intersection of [Formula: see text] with the corresponding terms of the [Formula: see text]-series of [Formula: see text], and the [Formula: see text]-length of [Formula: see text] may exceed the [Formula: see text]-length of [Formula: see text] by at most one. These theorems generalize the main results in [E. I. Khukhro, Fitting height of a finite group with a Frobenius group of automorphisms, J. Algebra 366 (2012) 1\u201311] obtained by Khukhro.<\/jats:p>","DOI":"10.1142\/s0218196720500319","type":"journal-article","created":{"date-parts":[[2020,2,4]],"date-time":"2020-02-04T07:34:58Z","timestamp":1580801698000},"page":"1073-1080","source":"Crossref","is-referenced-by-count":0,"title":["Frobenius action on Carter subgroups"],"prefix":"10.1142","volume":"30","author":[{"given":"G\u00fcli\u0307n","family":"Ercan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Middle East Technical University, Ankara, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u0130smai\u0307l \u015e.","family":"G\u00fclo\u011flu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Do\u011fu\u015f University, Istanbul, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,3,27]]},"reference":[{"key":"S0218196720500319BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02367023"},{"issue":"5","key":"S0218196720500319BIB002","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1515\/jgt-2014-0002","volume":"17","author":"Ercan G.","year":"2014","journal-title":"J. Group Theory"},{"key":"S0218196720500319BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s10469-014-9287-4"},{"key":"S0218196720500319BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196716500533"},{"key":"S0218196720500319BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s00605-016-0970-5"},{"key":"S0218196720500319BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2017.10.021"},{"key":"S0218196720500319BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2014.04.025"},{"key":"S0218196720500319BIB008","doi-asserted-by":"publisher","DOI":"10.3906\/mat-1403-62"},{"key":"S0218196720500319BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2014.01.005"},{"key":"S0218196720500319BIB010","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/092"},{"key":"S0218196720500319BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2012.05.011"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196720500319","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,26]],"date-time":"2023-09-26T06:09:36Z","timestamp":1695708576000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196720500319"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,27]]},"references-count":11,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2020,8]]}},"alternative-id":["10.1142\/S0218196720500319"],"URL":"https:\/\/doi.org\/10.1142\/s0218196720500319","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,27]]}}}