THE NORMAL INDEX OF A MAXIMAL SUBGROUP OF A FINITE ...

For a maximal subgroup M of a finite group G , the normal index r¡(G : M) is defined to be the order of a chief factor H/K where H is minimal in the set of ...

Index of a maximal subgroup in a finite group - Math Stack Exchange

If a group has the property that all its maximal subgroups have prime index, then it is solvable; this follows from a theorem of P. Hall.

THE NORMAL INDEX OF MAXIMAL SUBGROUPS - Project Euclid

In [4] Deskins defined the normal index of a maximal subgroup M in a finite group G as the order of a chief factor H/K of G where H is minimal.

On the normal index of maximal subgroups in finite groups

For a maximal subgroup M of a finite group G, the normal index of M is the order of a chief factor H/K where H is minimal in the set of ...

The normal index of a finite group

Thus G has a unique maximal normal subgroup and there is a common divisor of the indices of all the maximal subgroups with core (1). Therefore by using Baer [1, ...

on the normal index of maximal subgroups in finite groups ... - CORE

For a maximal subgroup M of a finite group G, the normal index of M is the order of a chief factor H/K where H is minimal in the set of normal supplements ...

The normal index of maximal subgroups in finite groups

The normal index of M, η(G : M), is the order of a chief factor H/K of G when H is a minimal supplement of M in G.

A Note on the Normal Index and the c‐Section of Maximal ...

Let M be a maximal subgroup of finite group G. For each chief factor H/K of G such that K ≤ M and G = MH, we called the order of H/K the ...

Does every finitely generated group have a maximal normal ...

If you mean nontrivial maximal normal subgroup (not 1 or the whole group), then the answer is no. Higman constructed a finitely generated ...

On the normal index and the c-section of maximal subgroups of a ...

Let M be a maximal subgroup of a finite group G . The order of a chief factor H/K such that H is a minimal supplement to M in G is called ...

A Note on the Normal Index and the c-Section of Maximal ...

Let M M be a maximal subgroup of finite group G G . For each chief factor H ... K H / K the normal index of M M and (M∩H)/K M ...

Maximal subgroup - Wikipedia

In group theory, a maximal subgroup H of a group G is a proper subgroup, such that no proper subgroup K contains H strictly.

Maximal normal subgroup - Groupprops

In a non-solvable group, maximal normal subgroups could either be normal of prime index or be normal subgroups with the quotient a simple non- ...

Maximal subgroups of solvable groups have prime power index

The statement being proved is that if H is a maximal proper subgroup of a finite solvable group G, then [G:H] is a prime power.

arXiv:1509.08090v1 [math.GR] 27 Sep 2015

(2) For every normal subgroup N < G, the quotient G/N is in MN. (3) All maximal subgroups of G are of finite index and all finite quotients of G ...

All maximal subgroups have odd index - MathOverflow

The maximal subgroups of A7 are A6 (index 7), S5 (index 21), (A4×A3):2 (index 35), and GL3(2) (index 15). If G is a nonabelian finite simple ...

On the Deskins index complex of a maximal subgroup of a finite group

CYW@~J.Y of M in G. Set P(M) ={C E f(M) 1 C is maximal in I(M) and G = CM}. The purpose of this note is to prove: A finite group G is solvable if and only ...

on the intersection of a family of maximal subgroups containing the ...

Deskins [6] has discussed the intersection of the family of maximal subgroups of a finite group whose indices are co-prime to a given prime. In [4-5, 12] we ...

On the Deskins index complex of a maximal subgroup of a finite group

Namely, if G is such a group, we call {\gamma_{0}(G)} the normal primary covering number of G; this is defined as the smallest positive integer k such that the ...

On the indices of maximal subgroups and the normal primary ...

We define and study two arithmetic functions γ0{\gamma_{0}} and η, having domain the set of all finite groups whose orders are not prime ...