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Conjugacy classes of maximal cyclic subgroups and nilpotence class of -groups
M. Bianchi, R. D. Camina, Mark L. Lewis
In this paper, we set to be the number of conjugacy classes of maximal cyclic subgroups of . We prove that if is a -group of order and nilpotence class ,…
Conjugacy classes of maximal cyclic subgroups
M. Bianchi, R. D. Camina, Mark L. Lewis +1
In this paper, we set to be the number of conjugacy classes of maximal cyclic subgroups of . We consider and direct and semi-direct products. We characterize the norm…
On solvable groups with one vanishing class size
Mariagrazia Bianchi, Rachel D. Camina, Mark L. Lewis +1
Let be a finite group, and let cs be the set of conjugacy class sizes of . Recalling that an element of is called a \emph{vanishing element} if there exists an…
Conjugacy class sizes in arithmetic progression
Mariagrazia Bianchi, Cheryl E. Praeger, S. P. Glasby
Let denote the set of conjugacy class sizes of a group , and let be the sizes of non-central classes. We prove three resu…
On vanishing class sizes in finite groups
Mariagrazia Bianchi, Julian M. A. Brough, Rachel D. Camina +1
Let be a finite group. An element of is called a vanishing element if there exists an irreducible character of such that ; in this case, we say that t…
Finite groups with non-trivial intersections of kernels of all but one irreducible characters
Mariagrazia Bianchi, Marcel Herzog
In this paper we consider finite groups G satisfying the following condition: G has two columns in its character table which differ by exactly one entry. It turns out that such gro…