More super p-groups

Finite groups have even more centralizers

For a finite group $G$‎, ‎let $Cent(G)$ denote the set of centralizers of single elements of $G$‎. ‎In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent‎, ‎then $Gcong S_3‎, ‎D_{10}$ or $S_3times S_3$‎. ‎This result gives a partial and positive answer to a conjecture raised by A‎. ‎R‎. ‎Ashrafi [On finite groups with a given number of centralizers‎, ‎Algebra‎ ‎Collo...

More on Super-replication Formulae

Abstract. We extend Norton-Borcherds-Koike’s replication formulae to super-replicable ones by working with the congruence groups Γ1(N) and find the product identities which characterize super-replicable functions. These will provide a clue for constructing certain new infinite dimensional Lie superalgebras whose denominator identities coincide with the above product identities. Therefore it cou...

More R-sequenceable Groups

More classes of super cycle-antimagic graphs

A simple graph G = (V,E) admits an H-covering if every edge in E belongs to a subgraph of G isomorphic to a given graph H . Then the graph G admitting an H-covering is (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2, . . . , |V | + |E|} such that, for all subgraphs ∗ Corresponding author. P. JAYANTHI ET AL. /AUSTRALAS. J. COMBIN. 67 (1) (2017), 46–64 47 H ′ of G isomorphic to H...

Some Properties of p-Groups and Commutative p-Groups

For simplicity, we use the following convention: G is a group, a, b are elements of G, m, n are natural numbers, and p is a prime natural number. One can prove the following propositions: (1) If for every natural number r holds n 6= pr, then there exists an element s of N such that s is prime and s | n and s 6= p. (2) For all natural numbers n, m such that n | pm there exists a natural number r...