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Kent State University

1. Croome, Sarah B. <i>p</i>-Group Codegree Sets and Nilpotence Class.

Degree: PhD, College of Arts and Sciences / Department of Mathematical Science, 2019, Kent State University

For a <i>p</i>-group <i>G</i> and an irreducible character χ of <i>G</i>, the codegree of χ is given by |<i>G</i>:ker(χ)|/χ(1). We investigate the relationship between the codegrees and nilpotence class of <i>p</i>-groups. If the set of codegrees of the irreducible characters of <i>G</i> has order 4, and <i>G</i> either has coclass at most 3, largest character degree <i>p</i>2, or |<i>G</i>:<i>G'</i>|=<i>p</i>2, then the nilpotence class of <i>G</i> is at most 4. Similar conditions exist which guarantee the existence of <i>p</i>2 as a codegree of <i>G</i>. If |<i>G</i>|=<i>pn</i> then cod(<i>G</i>) contains all powers of <i>p</i> up to <i>pn-1</i> if and only if <i>G</i> satisfies one of three cases in which <i>G</i> has maximal class or nilpotence class at most 2. We find families of maximal class groups which have consecutive <i>p</i>-power codegrees. Advisors/Committee Members: Lewis, Mark (Advisor).

Subjects/Keywords: Mathematics; groups; characters; codegrees; p-groups

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Croome, S. B. (2019). <i>p</i>-Group Codegree Sets and Nilpotence Class. (Doctoral Dissertation). Kent State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=kent1554462855786456

Chicago Manual of Style (16th Edition):

Croome, Sarah B. “<i>p</i>-Group Codegree Sets and Nilpotence Class.” 2019. Doctoral Dissertation, Kent State University. Accessed April 22, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=kent1554462855786456.

MLA Handbook (7th Edition):

Croome, Sarah B. “<i>p</i>-Group Codegree Sets and Nilpotence Class.” 2019. Web. 22 Apr 2019.

Vancouver:

Croome SB. <i>p</i>-Group Codegree Sets and Nilpotence Class. [Internet] [Doctoral dissertation]. Kent State University; 2019. [cited 2019 Apr 22]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=kent1554462855786456.

Council of Science Editors:

Croome SB. <i>p</i>-Group Codegree Sets and Nilpotence Class. [Doctoral Dissertation]. Kent State University; 2019. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=kent1554462855786456

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