Rank analogues of Hall's and Baer's theorems.
Recognition by the set of element orders of symmetric groups of degree and for prime .
Recognition of alternating groups of prime degree from their element orders.
Recognition of characteristically simple group by character degree graph and order
The character degree graph of a finite group is the graph whose vertices are the prime divisors of the irreducible character degrees of and two vertices and are joined by an edge if divides some irreducible character degree of . It is proved that some simple groups are uniquely determined by their orders and their character degree graphs. But since the character degree graphs of the characteristically simple groups are complete, there are very narrow class of characteristically simple...
Recognition of some linear groups over the binary field by the spectrum.
Recognition of the finite simple groups by the spectrum.
Recognition of the group from its spectrum.
Recognizability by spectrum of the group in the class of all groups.
Regular Orbits fo Hall ...-subgroups.
Remark on the multiplicity of a partition of a group into cosets
Representation of odd integers as the sum of one prime, two squares of primes and powers of 2