Certain embedding of the Burnside ring into its ghost ring
Character induction in p-groups.
Character Ramification and M-Groups.
Characterization by intersection graph of some families of finite nonsimple groups
For a finite group , , the intersection graph of , is a simple graph whose vertices are all nontrivial proper subgroups of and two distinct vertices and are adjacent when . In this paper, we classify all finite nonsimple groups whose intersection graphs have a leaf and also we discuss the characterizability of them using their intersection graphs.
Characterization of finite groups by their commuting graph.
Characterization of -solvable groups.
Characterization of by its non-commuting graph.
Characterization of the alternating groups by their order and one conjugacy class length
Let be a finite group, and let be the set of conjugacy class sizes of . By Thompson’s conjecture, if is a finite non-abelian simple group, is a finite group with a trivial center, and , then and are isomorphic. Recently, Chen et al. contributed interestingly to Thompson’s conjecture under a weak condition. They only used the group order and one or two special conjugacy class sizes of simple groups and characterized successfully sporadic simple groups (see Li’s PhD dissertation). In...
Characterization of the soluble one-generator totally saturated formations of finite groups.
Characterizing finite groups whose enhanced power graphs have universal vertices
Let be a finite group and construct a graph by taking as the vertex set of and by drawing an edge between two vertices and if is cyclic. Let be the set consisting of the universal vertices of along the identity element. For a solvable group , we present a necessary and sufficient condition for to be nontrivial. We also develop a connection between and when is divisible by two distinct primes and the diameter of is 2.
Characterizing the Sporadic Simple Group of Suzuki by a 2-Local Subgroup.
Characters and systems of subgroups.
Characters and the generalized Fitting subgroup
Characters of finite groups and divisibility problems. (Charaktere endlicher Gruppen und Teilbarkeitsfragen.)
Characters of Groups with Normal Extra Special Subgroups.
Charaktere endlicher Gruppen mit vorgegebenen Schurschen Indizes.
Charakterisierungen einiger Schunckklassen endlicher auflösbarer Gruppen II.
Chern Classes and Extraspecial Groups.
Classification of finite groups satisfying a minimal condition.
Classification of finite groups with many minimal subgroups and with the number of conjugacy classes of G/S(G) equal to 8.
In this paper we classify all the finite groups satisfying r(G/S(G))=8 and ß(G)=r(G) - a(G) - 1, where r(G) is the number of conjugacy classes of G, ß(G) is the number of minimal normal subgroups of G, S(G) the socle of G and a(G) the number of conjugacy classes of G out of S(G). These results are a contribution to the general problem of the classification of the finite groups according to the number of conjugacy classes.