Topics in Finite Groups

Gagen, T. M.

doi:10.1017/cbo9780511629266

Cited by 49 publications

(18 citation statements)

References 0 publications

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“…Our notation is standard and follows Gagen [3], Huppert [5] and Isaacs [7] when appropriate. Proof, By Theorem 2.1 K/Z is an elementary abelian p-group for some prime p. Consider the "bilinear" function ((,)): [7].…”

Section: -[G: Z(g)]mentioning

confidence: 99%

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In search of nonsolvable groups of central type

Liebler¹,

Yellen²

1979

Pacific J. Math.

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Section: -[G: Z(g)]mentioning

confidence: 99%

“…In the first case, inspection of the group order formulae leads to the possibilities: PSL (2, 8), PSL (3, 4), PSL(6, 2), PSP(6, 2), PΩ (5, 2), PΩ + (8, 2) and the solvable group PSU (3,2). For these groups, the primes r = 7, 5, 31, 5, 5 and 7 respectively satisfy hypothesis (1.1).…”

Section: Proof Suppose H ^ C G (K) and H/c G (K) = Psl (2 Q) Is A Cmentioning

confidence: 99%

In search of nonsolvable groups of central type

Liebler¹,

Yellen²

1979

Pacific J. Math.

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“…But P* = Cp. (LST) X P, by Gagen (1976), Corollary 0.5, and so C LST (P) = 1, as claimed. This completes the proof of 5.6, and, with it, the proof of Theorem A.…”

Section: Hall-closed Fitting Classes 153mentioning

confidence: 61%

Hall-closure and products of Fitting classes

Brison¹

1982

J Aust Math Soc A

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The Fitting class (of finite, soluble, groups), Of, is said to be Hall ir-closed (where IT is a set of primes) if whenever G is a group in g and H is a Hall w-subgroup of G, then H belongs to gf. In this paper, we study the Hall w-closure of products of Fitting classes. Our main result is a characterisation of the Hall w-closed Fitting classes of the form 2f#©^ (where <& m denotes the so-called smallest normal Fitting class), subject to a restriction connecting ir with the characteristic of g. We also characterise those Fitting classes g (respectively, ©) such that 3E#g (respectively, 5E)#3E) is Hall ir-closed for all Fitting classes X. In each case, part of the proof uses a concrete group construction. As a bonus, one of these constructions also yields a "cancellation result" for certain products of Fitting classes.

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“…[5,Theorem 5.3.4]), a generalization of a fundamental result of H. Bender (cf. [2,Satz] and [4,Theorem 3.1]) and a generalization of an important result of N. Blackburn (cf. [3,Theorem]).…”

Section: Generalizations Of Certain Fundamental Results On Finite Gromentioning

confidence: 99%