626 research outputs found
Almost all extraspecial p-groups are Swan groups
Let P be an extraspecial p-group which is neither dihedral of order 8, nor of
odd order p^3 and exponent p. Let G be a finite group having P as a Sylow
p-subgroup. Then the mod-p cohomology ring of G coincides with that of the
normalizer N_G(P).Comment: 5 page
Extendible characters and monomial groups of odd order
Let be a finite -solvable group, where is an odd prime. We
establish a connection between extendible irreducible characters of subgroups
of that lie under monomial characters of and nilpotent subgroups of
. We also provide a way to get ``good'' extendible irreducible characters
inside subgroups of . As an application, we show that every normal subgroup
of a finite monomial odd -group , that has nilpotent length less
than or equal to 3, is monomial
The continuity of -rationality and a lower bound for -degree characters of finite groups
Let be a prime and a finite group. We propose a strong bound for the
number of -degree irreducible characters of in terms of the commutator
factor group of a Sylow -subgroup of . The bound arises from a recent
conjecture of Navarro and Tiep [NT21] on fields of character values and a
phenomenon called the continuity of -rationality level of -degree
characters. This continuity property in turn is predicted by the celebrated
McKay-Navarro conjecture [Nav04]. We achieve both the bound and the continuity
property for .Comment: 22 pages. To appear in TAM
A characterization of the unitary and symplectic groups over finite fields of characteristic at least
The following characterization is obtained:
THEOREM. Let G be a finite group generated by a conjugacy class D of subgroups of prime order p ^ 5, such that for any choice of distinct A and B in D, the subgroup generated by A and B is isomorphic to Zp x Zp, L2(pm) or SL2(pm), where m depends on A and B. Assume G has no nontrivial solvable normal subgroup. Then G is isomorphic to Spn(q) or Un(q) for some power q of p
On the characters of the Sylow p-subgroups of untwisted Chevalley groups Y_n(p^a)
Let be a Sylow p-subgroup of an untwisted Chevalley group
of rank n defined over where q is a power of a prime p. We
partition the set of irreducible characters of into
families indexed by antichains of positive roots of the root system of type
. We focus our attention on the families of characters of which
are indexed by antichains of length 1. Then for each positive root we
establish a one to one correspondence between the minimal degree members of the
family indexed by and the linear characters of a certain subquotient
of . For our single root character
construction recovers amongst other things the elementary supercharacters of
these groups. Most importantly though this paper lays the groundwork for our
classification of the elements of , and
Radical \u3cem\u3ep\u3c/em\u3e-chains in L\u3csub\u3e3\u3c/sub\u3e(2).
The McKay-Alperin-Dade Conjecture, which has not been finally verified, predicts the number of complex irreducible characters in various p-blocks of a finite group G as an alternating sum of the numbers of characters in related p-blocks of certain subgroups of G. The sub-groups involved are the normalizers of representatives of conjugacy classes of radical p-chains of G. For this reason, it is of interest to study radical p-chains. In this thesis, we examine the group L3(2) and determine representatives of the conjugacy classes of radical p-subgroups and radical p-chains for the primes p = 2, 3, and 7. We then determine the structure of the normalizers of these subgroups and chains
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