Finite groups with sylow 2-subgroups of type the alternating group of degree sixteen

2006 ◽  
pp. 730-732
Author(s):  
Hiroyoshi Yamaki
Keyword(s):  
Finite Groups ◽  
Alternating Group

scholarly journals Projective modular representations of finite groups II

1981 ◽  
Vol 22 (1) ◽  
pp. 89-99 ◽  
Author(s):  
J. F. Humphreys
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Theoretical Background ◽  
Alternating Group ◽  
Modular Representations ◽  
Future Paper ◽  
Representations Of Finite Groups ◽  
Group A ◽  
Mathieu Groups

In this paper, which is a continuation of [4], the necessary theoretical background is given to enable the calculation of the irreducible Brauer projective characters of a given finite group to be carried out. As an example, this calculation is done for the alternating group A (7) in §3. In a future paper the calculations for the Mathieu groups will be presented.

Integral Cayley Graphs over Finite Groups

2020 ◽  
Vol 27 (01) ◽  
pp. 131-136
Author(s):  
Elena V. Konstantinova ◽  
Daria Lytkina
Keyword(s):  
Finite Group ◽  
Symmetric Group ◽  
Cayley Graph ◽  
Cyclic Group ◽  
Finite Groups ◽  
Cayley Graphs ◽  
Alternating Group ◽  
Generating Set ◽  
A Finite Group

We prove that the spectrum of a Cayley graph over a finite group with a normal generating set S containing with every its element s all generators of the cyclic group 〈s〉 is integral. In particular, a Cayley graph of a 2-group generated by a normal set of involutions is integral. We prove that a Cayley graph over the symmetric group of degree n no less than 2 generated by all transpositions is integral. We find the spectrum of a Cayley graph over the alternating group of degree n no less than 4 with a generating set of 3-cycles of the form (k i j) with fixed k, as {−n+1, 1−n+1, 22 −n+1, …, (n−1)2 −n+1}.

Size of free groups in varieties generated by finite groups

2019 ◽  
Vol 29 (08) ◽  
pp. 1419-1430
Author(s):  
William Cocke
Keyword(s):  
Finite Group ◽  
Free Group ◽  
Finite Groups ◽  
Prime Order ◽  
Free Groups ◽  
Affine Group ◽  
Alternating Group ◽  
A Finite Group

The number of distinct [Formula: see text]-variable word maps on a finite group [Formula: see text] is the order of the rank [Formula: see text] free group in the variety generated by [Formula: see text]. For a group [Formula: see text], the number of word maps on just two variables can be quite large. We improve upon previous bounds for the number of word maps over a finite group [Formula: see text]. Moreover, we show that our bound is sharp for the number of 2-variable word maps over the affine group over fields of prime order and over the alternating group on five symbols.

scholarly journals EXTENSION OF AUTOMORPHISMS OF SUBGROUPS

2012 ◽  
Vol 54 (2) ◽  
pp. 371-380
Author(s):  
G. G. BASTOS ◽  
E. JESPERS ◽  
S. O. JURIAANS ◽  
A. DE A. E SILVA
Keyword(s):  
Abelian Group ◽  
Finite Groups ◽  
Dihedral Group ◽  
Abelian Groups ◽  
Alternating Group ◽  
Finite Abelian Groups ◽  
Quaternion Group ◽  
Icosahedral Group ◽  
Odd Order ◽  
Even Order

AbstractLet G be a group such that, for any subgroup H of G, every automorphism of H can be extended to an automorphism of G. Such a group G is said to be of injective type. The finite abelian groups of injective type are precisely the quasi-injective groups. We prove that a finite non-abelian group G of injective type has even order. If, furthermore, G is also quasi-injective, then we prove that G = K × B, with B a quasi-injective abelian group of odd order and either K = Q8 (the quaternion group of order 8) or K = Dih(A), a dihedral group on a quasi-injective abelian group A of odd order coprime with the order of B. We give a description of the supersoluble finite groups of injective type whose Sylow 2-subgroup are abelian showing that these groups are, in general, not quasi-injective. In particular, the characterisation of such groups is reduced to that of finite 2-groups that are of injective type. We give several restrictions on the latter. We also show that the alternating group A5 is of injective type but that the binary icosahedral group SL(2, 5) is not.

Finite groups with exactly one composite character degree

2016 ◽  
Vol 15 (07) ◽  
pp. 1650132 ◽  
Author(s):  
Yan-Jun Liu ◽  
Yang Liu
Keyword(s):  
Finite Groups ◽  
Character Degree ◽  
Alternating Group ◽  
Direct Factor ◽  
Irreducible Characters

Motivated by Isaacs and Passman’s characterization of finite groups all of whose nonlinear complex irreducible characters have prime degrees, we investigate finite groups [Formula: see text] with exactly one character degree that is not a prime. We show that either [Formula: see text] is solvable with [Formula: see text] or [Formula: see text] for distinct primes [Formula: see text], or up to an abelian direct factor, [Formula: see text] is isomorphic to the alternating group [Formula: see text].

scholarly journals Factorization of groups involving symmetric and alternating groups

2001 ◽  
Vol 27 (3) ◽  
pp. 161-167 ◽  
Author(s):  
M. R. Darafsheh ◽  
G. R. Rezaeezadeh
Keyword(s):  
Symmetric Group ◽  
Finite Groups ◽  
Alternating Group ◽  
Alternating Groups

We obtain the structure of finite groups of the formG=ABwhereBis a group isomorphic to the symmetric group onnlettersSn,n≥5andAis a group isomorphic to the alternating group on 6 letters.

OD-Characterization of Certain Finite Groups Having Connected Prime Graphs

2010 ◽  
Vol 17 (01) ◽  
pp. 121-130 ◽  
Author(s):  
A. R. Moghaddamfar ◽  
A. R. Zokayi
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Symmetric Group ◽  
Finite Groups ◽  
Alternating Group ◽  
Degree Pattern ◽  
Prime Graphs ◽  
Group A ◽  
A Finite Group

The degree pattern of a finite group G denoted by D(G) was introduced in [5]. We say that G is k-fold OD-characterizable if there exist exactly k non-isomorphic finite groups having the same order and same degree pattern as G. In the present article, we show that the alternating group A10 and the automorphism group Aut (McL) are 2-fold OD-characterizable, while the automorphism group Aut (J2) is 3-fold OD-characterizable and the symmetric group S10 is 8-fold OD-characterizable. It is worth mentioning that the prime graphs associated to these groups are connected and, in fact, among the groups with this property, they are the first groups which are investigated for OD-characterizability.

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