Let Gp be a Sylow p-subgroup of the finite groupG and let Char G n (Gp) represent the set of degree n complex characters of Gp that are the restrictions of class functions on G. We construct a natural map ψG : [BG,BU(n)] → ∏ p||G| Char G n (Gp) and prove that ψG is a surjection for all finite groups G that do not contain a subgroup isomorphic to (Z/p) for any prime p. We show, furthermore, that...

Let E be an optimal elliptic curve overQ of prime conductorN . We show that if for an odd prime p, the mod p representation associated to E is reducible (in particular, if p divides the order of the torsion subgroup of E(Q)), then the p-primary component of the ShafarevichTate group of E is trivial. We also state a related result for more general abelian subvarieties of J0(N) and mention what t...

let $g$ be a finite group‎. ‎a subgroup‎ ‎$h$ of $g$ is called an $mathcal{h}$-subgroup in‎ ‎$g$ if $n_g(h)cap h^{g}leq h$ for all $gin‎ ‎g$. a subgroup $h$ of $g$ is called a weakly‎ ‎$mathcal{h}^{ast}$-subgroup in $g$ if there exists a‎ ‎subgroup $k$ of $g$ such that $g=hk$ and $hcap‎ ‎k$ is an $mathcal{h}$-subgroup in $g$. we‎ ‎investigate the structure of the finite group $g$ under the‎ ‎as...

Let p be any prime. P n a Sylow -subgroup of the symmetric group S . ϕ and ψ linear characters let N normaliser in In this article we show that inductions to are equal if, only –conjugate. This is an analogue for groups result Navarro -solvable groups.

‎motivated by a celebrated theorem of schur‎, ‎we show that if~$gamma$ is a normal subgroup of the full automorphism group $aut(g)$ of a group $g$ such that $inn(g)$ is contained in $gamma$ and $aut(g)/gamma$ has no uncountable abelian subgroups of prime exponent‎, ‎then $[g,gamma]$ is finite‎, ‎provided that the subgroup consisting of all elements of $g$ fixed by $gamma$ has finite index‎. ‎so...

We demonstrate that two supersoluble complements of an abelian base in a finite split extension are conjugate if and only if, for each prime $p$, Sylow $p$-subgroup one complement is to the other. As corollary, we find any subgroup $N$ $G$ there exists $S$ such $S\cap N$ $G$. In particular, restricting groups allows us ease D. G. Higman's stipulation be within $S$. then consider group actions o...

For any positive integer N, we completely determine the structure of rational cuspidal divisor class group X0(N), which is conjecturally equal to torsion subgroup J0(N). More specifically, for a given prime ℓ, construct Zℓ(d) non-trivial d N. Also, compute order linear equivalence and show that ℓ-primary X0(N) isomorphic direct sum cyclic subgroups generated by classes Zℓ(d).

a subgroup $h$ is said to be $s$-permutable in a group $g$‎, ‎if‎ ‎$hp=ph$ holds for every sylow subgroup $p$ of $g$‎. ‎if there exists a‎ ‎subgroup $b$ of $g$ such that $hb=g$ and $h$ permutes with every‎ ‎sylow subgroup of $b$‎, ‎then $h$ is said to be $ss$-quasinormal in‎ ‎$g$‎. ‎in this paper‎, ‎we say that $h$ is a weakly $ss$-quasinormal‎ ‎subgroup of $g$‎, ‎if there is a normal subgroup ...

If G is a finite group and N is a normal subgroup of G with two Gconjugacy class sizes of elements of prime power order, then we show that N is nilpotent.