Powers and products of conjugacy classes in groups

Arad, Zvi; Stavi, Jonathan; Herzog, Marcel

doi:10.1007/bfb0072286

Cited by 56 publications

(77 citation statements)

References 8 publications

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“…The covering number, cn(G), of a group G is the smallest positive integer n, such that C = G for all non-identity conjugacy classes, C, of G. If no such integer exists we say that the covering number is infinite. The notion of a covering number was mentioned in [3] where it is shown:…”

Section: Ii) (Dd 2 D 3 ) = \D 2 \ \D 3 \-'{D^ \D 2 -»)mentioning

confidence: 99%

An analogy between products of two conjugacy classes and products of two irreducible characters in finite groups

Arad

Fisman

1987

Proceedings of the Edinburgh Mathematical Society

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Section: Ii) (Dd 2 D 3 ) = \D 2 \ \D 3 \-'{D^ \D 2 -»)mentioning

confidence: 99%

An analogy between products of two conjugacy classes and products of two irreducible characters in finite groups

Arad

Fisman

1987

Proceedings of the Edinburgh Mathematical Society

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“…The result that the factor groups HI = Sl+1 /SI (0 < t < v) are simple has recently been sharpened in two directions. First, Moran [21,22] and Arad, Chillag and Moran [1] have shown that for any non-unit conjugacy class C in HI (0 < r < v), in fact HJV -C2 if v > 0, and HI = C3 if v = 0. Secondly, Droste and Göbel [13] (and Bertram [5] if v = 0)…”

Section: Squares Of Conjugacy Classes In the Infinite Symmetric Groupmentioning

confidence: 99%

“…In [10] we showed that any infinite group G can be embedded into a simple group H of the same cardinality satisfying H = C2 for each nonunit conjugacy class C in H. Here we wish to sharpen this result. For background information and a variety of recent theorems in this area we refer the reader to [1,2,16,21,22]. We will use the following result related to Lemma 5.1.…”

Section: Proof Of Theoremmentioning

confidence: 99%

Squares of Conjugacy Classes in the Infinite Symmetric Groups

Droste¹

1987

Transactions of the American Mathematical Society

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ABSTRACT.Using combinatorial methods, we will examine squares of conjugacy classes in the symmetric groups Su of all permutations of an infinite set of cardinality N^. For arbitrary permutations p G Si,, we will characterize when each element s € Sv with finite support can be written as a product of two conjugates of p, and if p has infinitely many fixed points, we determine when all elements of S" are products of two conjugates of p. Classical group-theoretical theorems are obtained from similar results.

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“…From (2) and (3) Finally, let -k -7r(n) and suppose that |G/Z(x)U ^ 1. Let gZ(x) be a nonidentity 7r-element of G/Z(x)-Then gn' G Z(x) for some positive integer j.…”

Section: Proof Of Theorem A(i)mentioning

confidence: 99%

“…The book [1] (in particular, the articles [2 and 3]) and the article [4] contain analogous results on the so-called covering number and character-covering-number of a finite group. The identity C\C2 -C\, C2 or C\ U C2 for two nonidentity conjugacy classes Gi, C2 of G, and the condition Irr(xiX2) Q {xiiX2} for two nonprincipal irreducible characters XiiX2 of G, axe investigated in the forthcoming articles [5 and 10], and an extension of the character-theoretic results to modular representations is studied in [6].…”

Section: Introductionmentioning

confidence: 99%