Formation theory in locally finite groups satisfying min-p for all primes p

Outer Automorphisms of Locally Finite p-Groups∗

Every group is an outer automorphism group of a locally finite p-group. This extends an earlier result [3] about countable outer automorphism groups. It is also in sharp contrast to results concerning the existence of outer automorphisms of nilpotent groups in [6, 13, 14].

locally finite p-groups with all subgroups either subnormal or nilpotent-by-chernikov

‎we pursue further our‎ ‎investigation‎, ‎begun in [h.~smith‎, ‎groups with all subgroups subnormal or‎ ‎nilpotent-by-{c}hernikov‎, ‎emph{rend‎. ‎sem‎. ‎mat‎. ‎univ‎. ‎padova}‎ ‎126 (2011)‎, ‎245--253] and continued in [g.~cutolo and h.~smith‎, ‎locally finite groups with all subgroups‎ ‎subnormal or nilpotent-by-{c}hernikov‎. ‎emph{centr‎. ‎eur‎. ‎j‎. ‎math.} (to appear)] ‎‎‎of groups $g$ in w...

FINITE p-GROUPS IN REPRESENTATION THEORY

ARE PSEUDOPRIMES FOR ALMOST ALL PRIMES p

It was proven by Emma Lehmer that for almost all odd primes p, F2p is a Fibonacci pseudoprime. In this paper, we generalize this result to Lucas sequences {Uk}. In particular, we find Lucas sequences {Uk} for which either U2p is a Lucas pseudoprime for almost all odd primes p or Up is a Lucas pseudoprime for almost all odd primes p.

Finite Groups with p-Sylow Coverings