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Burkett, Shawn, Lewis, Mark. (1401). A characterization of GVZ groups in terms of fully ramified characters. , 11(2), 121-124. doi: 10.22108/ijgt.2021.127210.1673
Shawn T. Burkett; Mark L. Lewis. "A characterization of GVZ groups in terms of fully ramified characters". , 11, 2, 1401, 121-124. doi: 10.22108/ijgt.2021.127210.1673
Burkett, Shawn, Lewis, Mark. (1401). 'A characterization of GVZ groups in terms of fully ramified characters', , 11(2), pp. 121-124. doi: 10.22108/ijgt.2021.127210.1673
Burkett, Shawn, Lewis, Mark. A characterization of GVZ groups in terms of fully ramified characters. , 1401; 11(2): 121-124. doi: 10.22108/ijgt.2021.127210.1673

A characterization of GVZ groups in terms of fully ramified characters

International Journal of Group Theory
دوره 11، شماره 2، شهریور 2022، صفحه 121-124    اصل مقاله (174.6 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2021.127210.1673
نویسندگان
Shawn T. Burkett؛ Mark L. Lewis*
Department of Mathematical Sciences, Kent State University Kent, Ohio 44242, U.S.A.
چکیده
In this paper‎, ‎we obtain a characterization of GVZ-groups in terms of commutators and monolithic quotients‎. ‎This characterization is based on counting formulas due to Gallagher‎.
کلیدواژه‌ها
‎GVZ groups؛ $p$-groups؛ fully ramified characters
مراجع
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[2] S. T. Burkett and M. L. Lewis, GVZ-groups, flat groups, and CM-groups, C. R. Math. Acad. Sci. Paris, 359 (2021)
355–361.

[3] S. T. Burkett and M. L. Lewis, Partial GVZ-groups, J. Algebra, 581 (2021) 50–62.

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(1969) 145–153.

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[8] I. M. Isaacs, Character theory of finite groups, Dover Publications, Inc., New York, 1994.

[9] I. M. Isaacs, Characters of solvable groups, American Mathematical Society, Providence, RI, 2018.

[10] M. L. Lewis, Groups where the centers of the irreducible characters form a chain, Monatsh. Math., 192 (2020) 371–399.

[11] M. Murai, Characterizations of p-nilpotent groups, Osaka J. Math., 31 (1994) 1–8.

[12] A. Nenciu, Isomorphic character tables of nested GVZ-groups, J. Algebra Appl., 11 (2012) 12 pp.

[13] A. Nenciu, Nested GVZ-groups, J. Group Theory, 19 (2016) 693–704.

[14] H. Tandra, and W. Moran, Flatness conditions on finite p-groups, Comm. Algebra, 32 (2004) 2215–2224.

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