7 papers
On abelian subgroups of finite groups
Avinoam Mann
We consider abelain subgroups of small index in finite groups. More generally, we consider subgroups such that the product of their index by the index of their centralizer is small…
Explicit universal minimal constants for polynomial growth of groups
Russell Lyons, Avinoam Mann, Romain Tessera +1
Shalom and Tao showed that a polynomial upper bound on the size of a single, large enough ball in a Cayley graph implies that the underlying group has a nilpotent subgroup with ind…
The breadth-degree type of a finite -group
Norberto Gavioli, Avinoam Mann, Valerio Monti
We determine an upper bound for the size of a stem -group in terms of its breadth and its maximum character degree.
Character degrees of some -groups
Avinoam Mann
We restrict the possibilities for the character degrees of -groups satisfying . E.g. if is of maximal class and has an irreducible character of degree $> p…
Some group theoretical mass formulae
Avinoam Mann
A 'mass formula' is a formula involving a sum of reciprocals of automorphism groups orders. We provide several such formulae, e.g. ones involving covering groups of finite groups.…
Philip Hall's 'rather curious' formula and the Rogers-Ramanujan identities
Avinoam Mann
We show that a strange group theoretical formula of Hall follows from the Rogers-Ramanujan identities.
Automorphism groups of covering groups
Avinoam Mann
We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.