scholarly journals The automorphism group of a p-group of maximal class with an abelian maximal subgroup

1976 ◽  
Vol 93 (1) ◽  
pp. 41-46 ◽  
Author(s):  
Alphonse Baartmans ◽  
James Woeppel
Keyword(s):  
Automorphism Group ◽  
Maximal Subgroup ◽  
Maximal Class

The Fischer-Clifford Matrices and Character Table of a Maximal Subgroup of Fi24

2010 ◽  
Vol 17 (03) ◽  
pp. 389-414 ◽  
Author(s):  
Faryad Ali ◽  
Jamshid Moori
Keyword(s):  
Automorphism Group ◽  
Conjugacy Class ◽  
Maximal Subgroup ◽  
Computer Algebra ◽  
Character Table ◽  
Computer Algebra Systems ◽  
Split Extension ◽  
Sporadic Group ◽  
Local Subgroup ◽  
Fischer Group

The Fischer group [Formula: see text] is the largest 3-transposition sporadic group of order 2510411418381323442585600 = 222.316.52.73.11.13.17.23.29. It is generated by a conjugacy class of 306936 transpositions. Wilson [15] completely determined all the maximal 3-local subgroups of Fi24. In the present paper, we determine the Fischer-Clifford matrices and hence compute the character table of the non-split extension 37· (O7(3):2), which is a maximal 3-local subgroup of the automorphism group Fi24 of index 125168046080 using the technique of Fischer-Clifford matrices. Most of the calculations are carried out using the computer algebra systems GAP and MAGMA.

scholarly journals Some bounds for the degree of commutativity of a p-group of maximal class

1995 ◽  
Vol 51 (3) ◽  
pp. 353-367
Author(s):  
Antonio Vera-López ◽  
Gustavo A. Fernández-Alcober
Keyword(s):  
Maximal Subgroup ◽  
Lower Bounds ◽  
Nilpotency Class ◽  
The Other ◽  
Maximal Class ◽  
Derived Length ◽  
Other Hand

In this paper we obtain several lower bounds for the degree of commutativity of a p-group of maximal class of order pm. All the bounds known up to now involve the prime p and are almost useless for small m. We introduce a new invariant b which is related with the commutator structure of the group G and get a bound depending only on b and m, not on p. As a consequence, we bound the derived length of G and the nilpotency class of a certain maximal subgroup in terms of b. On the other hand, we also generalise some results of Blackburn. Examples are given in order to check the sharpness of the bounds.

On a maximal subgroup $$(2^9{:}(L_3(4)){:}3$$ of the automorphism group $$U_6(2){:}3$$ of $$U_6(2)$$

2020 ◽  
Vol 31 (7-8) ◽  
pp. 1311-1336
Author(s):  
Abraham Love Prins ◽  
Ramotjaki Lucky Monaledi ◽  
Richard Llewellyn Fray
Keyword(s):  
Automorphism Group ◽  
Maximal Subgroup

Some finite p-groups with central automorphism group of minimal order

2019 ◽  
Vol 19 (09) ◽  
pp. 2050167
Author(s):  
Mehdi Shabani-Attar
Keyword(s):  
Automorphism Group ◽  
Maximal Subgroup ◽  
Minimal Order ◽  
Central Automorphism ◽  
Special Cases ◽  
Inner Automorphism ◽  
Central Automorphisms

Let [Formula: see text] be a finite [Formula: see text]-group and let [Formula: see text] be the set of all central automorphisms of [Formula: see text] For any group [Formula: see text], the center of the inner automorphism group, [Formula: see text], is always contained in [Formula: see text] In this paper, we study finite [Formula: see text]-groups [Formula: see text] for which [Formula: see text] is of minimal possible, that is [Formula: see text] We characterize the groups in some special cases, including [Formula: see text]-groups [Formula: see text] with [Formula: see text], [Formula: see text]-groups with an abelian maximal subgroup, metacyclic [Formula: see text]-groups with [Formula: see text], [Formula: see text]-groups of order [Formula: see text] and exponent [Formula: see text] and Camina [Formula: see text]-groups.

scholarly journals Fischer-Clifford Matrices and Character Table of the Maximal Subgroup (29:(L3(4)):2 of U6(2):2

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Abraham Love Prins ◽  
Ramotjaki Lucky Monaledi
Keyword(s):  
Automorphism Group ◽  
Maximal Subgroup ◽  
Unitary Group ◽  
Character Table ◽  
Split Extension ◽  
Parent Group ◽  
Extension Group ◽  
Clifford Theory

The automorphism group U6(2):2 of the unitary group U6(2)≅Fi21 has a maximal subgroup G¯ of the form (29:(L3(4)):2 of order 20643840. In this paper, Fischer-Clifford theory is applied to the split extension group G¯ to construct its character table. Also, class fusion from G¯ into the parent group U6(2):2 is determined.

The Modular Group Algebras of P-Groups of Maximal Class

1988 ◽  
Vol 40 (6) ◽  
pp. 1422-1435 ◽  
Author(s):  
C. Bagiński ◽  
A. Caranti
Keyword(s):  
Maximal Subgroup ◽  
Modular Group ◽  
Isomorphism Problem ◽  
Group Algebras ◽  
Maximal Class ◽  
Special Classes

The isomorphism problem for modular group algebras of finite p-groups appears to be still far from a solution (see [7] for a survey of the existing results). It is therefore of interest to investigate the problem for special classes of groups.The groups we consider here are the p-groups of maximal class, which were extensively studied by Blackburn [1]. In this paper we solve the modular isomorphism problem for such groups of order not larger than pp+1, having an abelian maximal subgroup, for odd primes p.What we in fact do is to generalize methods used by Passman [5] to solve the isomorphism problem for groups of order p4. In Passman's paper the case of groups of maximal class is actually the most difficult one.

scholarly journals AUTOMORPHISMS OF METABELIAN PRIME POWER ORDER GROUPS OF MAXIMAL CLASS

2008 ◽  
Vol 77 (2) ◽  
pp. 261-276
Author(s):  
S. FOULADI ◽  
R. ORFI
Keyword(s):  
Automorphism Group ◽  
Prime Power ◽  
Structure Theorem ◽  
Maximal Class ◽  
Prime Power Order ◽  
Full Automorphism Group ◽  
Maximum Value

AbstractLet G be a p-group of maximal class of order pn. It is shown that the order of the group of all automorphisms of G centralizing the Frattini quotient takes the maximum value p2n−4 if and only if G is metabelian. A structure theorem is proved for the Sylow p-subgroup, Autp(G), of the automorphism group of G when G is metabelian. For p=2, Aut2(G) is the full automorphism group of G. For p=3, we prove a structure theorem for the full automorphism group of G.

scholarly journals On the automorphism group of a symplectic half-flat 6-manifold

2019 ◽  
Vol 31 (1) ◽  
pp. 265-273
Author(s):  
Fabio Podestà ◽  
Alberto Raffero
Keyword(s):  
Automorphism Group ◽  
Lie Algebra ◽  
Group Action ◽  
Cohomogeneity One ◽  
Cohomogeneity One Action

Abstract We prove that the automorphism group of a compact 6-manifold M endowed with a symplectic half-flat {\mathrm{SU}(3)} -structure has Abelian Lie algebra with dimension bounded by {\min\{5,b_{1}(M)\}} . Moreover, we study the properties of the automorphism group action and we discuss relevant examples. In particular, we provide new complete examples on {T\mathbb{S}^{3}} which are invariant under a cohomogeneity one action of {\mathrm{SO}(4)} .

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