‎Let $G$ be a finite group and $nu(G)$ denote the number of conjugacy classes of non-normal subgroups of $G$‎. ‎In this paper‎, ‎all nilpotent groups $G$ with $nu(G)=3$ are classified‎.  

We classify the real and strongly real conjugacy classes in GLnðqÞ and SLnðqÞ. In each case we give a formula for the number of real, and the number of strongly real, conjugacy classes. This paper is the first of two that together classify the real and strongly real classes in GLnðqÞ, SLnðqÞ, PGLnðqÞ, PSLnðqÞ, and all quasi-simple covers of PSLnðqÞ.

The algebraic classification of Cardy for boundary states on a G/H coset CFT of a compact group G, is geometrically realized on the corresponding manifold resulting from gauging the WZW model. The branes consist of H orbits of quantized G conjugacy classes shifted by quantized H conjugacy classes.

We classify the real and strongly real conjugacy classes in GLn(q), SLn(q), PGLn(q), PSLn(q), and all quasi-simple covers of PSLn(q). In each case we give a formula for the number of real, and the number of strongly real, conjugacy classes.

Abstract In this chapter, we give a spectral characterisation of isomorphism induced representations. We also discuss strong isospectrality in the sense Pesce (which, by result Sunada, is implied weak conjugacy subgroups), an illustrative example lens spaces due to Ikeda, and use first conjugacy.

Generalized conjugation is the action of a group on its underlying set given by (g, x) 7→ φ(g)xg, where φ : G → G is some fixed endomorphism. Here we study combinatorial properties of the sizes of the orbits of the preceding action. In particular, we reduce the problem to a simpler case if φ has a nontrivial kernel or if it is an inner automorphism, and we give a construction that allows a part...

We consider three theorems in ergodic theory concerning a fixed aperiodic measure preserving transformation σ of a Lebesgue probability space (X,A, μ) and show that these theorems are all equivalent. Two of these results concern the existence of a partition of the space X with special properties. The third theorem asserts that the conjugates of σ are dense in the uniform topology on the space o...

We present a characterisation of conjugacy in Thompson’s group using the natural action of F on the interval [0, 1]. This characterisation completes the program begun by Brin and Squier [BS01]. Our characterisation also provides another solution to the conjugacy problem in Thompson’s group which was first solved by Guba and Sapir using diagram groups [GS97]. A number of other solutions exist du...

It is observed that the conjugacy growth series of the infinite finitary symmetric group with respect to the generating set of transpositions is the generating series of the partition function. Other conjugacy growth series are computed, for other generating sets, for restricted permutational wreath products of finite groups by the finitary symmetric group, and for alternating groups. Similar m...

For a finite group G we define the graph Γ(G) to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes A, B are joined by an edge if for some A ∈ A, B ∈ B A and B permute. We characterise those groups G for which