LAUSR

Testing Isomorphism of Central Cayley Graphs Over Almost Simple Groups in Polynomial Time

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1 Published in 2017 at "Journal of Mathematical Sciences"

DOI: 10.1007/s10958-018-3998-3

Abstract: A Cayley graph over a group G is said to be central if its connection set is a normal subset of G. It is proved that for any two central Cayley graphs over explicitly given… read more here.

Keywords: simple groups; almost simple; time; cayley graphs ... See more keywords

Regular orbits of sporadic simple groups

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1 Published in 2019 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2018.11.034

Abstract: Abstract Given a finite group G and a faithful irreducible FG-module V where F has prime order, does G have a regular orbit on V? This problem is equivalent to determining which primitive permutation groups… read more here.

Keywords: simple groups; group; orbits sporadic; sporadic simple ... See more keywords

Lübeck's classification of representations of finite simple groups of Lie type and the inverse Galois problem for some orthogonal groups

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1 Published in 2017 at "Journal of Number Theory"

DOI: 10.1016/j.jnt.2019.06.010

Abstract: Abstract In this paper we prove that for each integer of the form n = 4 ϖ (where ϖ is a prime between 17 and 73) at least one of the following groups: P Ω… read more here.

Keywords: groups lie; simple groups; galois; lie type ... See more keywords

An approach to Quillen’s conjecture via centralisers of simple groups

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1 Published in 2021 at "Forum of Mathematics, Sigma"

DOI: 10.1017/fms.2021.41

Abstract: Abstract For any given subgroup H of a finite group G, the Quillen poset ${\mathcal {A}}_p(G)$ of nontrivial elementary abelian p-subgroups is obtained from ${\mathcal {A}}_p(H)$ by attaching elements via their centralisers in H. We… read more here.

Keywords: simple groups; quillen conjecture; conjecture; via centralisers ... See more keywords

Blocks of small defect in symmetric and simple groups

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2 Published in 2018 at "Communications in Algebra"

DOI: 10.1080/00927872.2017.1411491

Abstract: ABSTRACT Let p be a prime, G a finite group, and r≥1. We say a p-block B with defect group D of G is r-small if . In this paper, we show that almost all… read more here.

Keywords: simple groups; blocks small; defect symmetric; small defect ... See more keywords

Exact Factorizations of Sporadic Simple Groups

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1 Published in 2019 at "Experimental Mathematics"

DOI: 10.1080/10586458.2018.1556137

Abstract: A group G is said to have an exact factorization if there exist proper subgroups Ai for i=1,2,…,n such that G=A1A2…An and |G|=|A1||A2|…|An|. The number n is called length of this factorization. An ... read more here.

Keywords: simple groups; sporadic simple; exact factorizations; factorizations sporadic ... See more keywords

Rapid growth in finite simple groups

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2 Published in 2017 at "Transactions of the American Mathematical Society"

DOI: 10.1090/tran/6935

Abstract: We show that small normal subsets A of finite simple groups grow very rapidly – namely, |A| ≥ |A|2− , where > 0 is arbitrarily small. Extensions, consequences, and a rapid growth result for simple… read more here.

Keywords: simple groups; mathematics; growth finite; rapid growth ... See more keywords

The FSZ properties of sporadic simple groups

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1 Published in 2019 at "Journal of Algebra and Its Applications"

DOI: 10.1142/s0219498819500166

Abstract: We investigate a possible connection between the [Formula: see text] properties of a group and its Sylow subgroups. We show that the simple groups [Formula: see text] and [Formula: see text], as well as all… read more here.

Keywords: sporadic simple; sylow subgroups; simple groups; formula see ... See more keywords

Free subgroups of inverse limits of iterated wreath products of non-abelian finite simple groups in primitive actions

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1 Published in 2017 at "Journal of Group Theory"

DOI: 10.1515/jgth-2016-0061

Abstract: Abstract Let ???? = { G i ∣ 1 ≤ i ∈ ℕ } {\mathcal{W}=\{G_{i}\mid 1\leq i\in\mathbb{N}\}} be a set of non-abelian finite simple groups. Set W 1 = G 1 {W_{1}=G_{1}} and choose a… read more here.

Keywords: simple groups; abelian finite; non abelian; finite simple ... See more keywords

Almost simple groups with no product of two primes dividing three character degrees

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1 Published in 2019 at "Journal of Group Theory"

DOI: 10.1515/jgth-2018-0188

Abstract: Abstract Let Irr⁡(G){\operatorname{Irr}(G)} denote the set of complex irreducible characters of a finite group G, and let cd⁡(G){\operatorname{cd}(G)} be the set of degrees of the members of Irr⁡(G){\operatorname{Irr}(G)}. For positive integers k and l, we… read more here.

Keywords: groups product; two primes; almost simple; product two ... See more keywords

Steinberg-like characters for finite simple groups

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1 Published in 2019 at "Journal of Group Theory"

DOI: 10.1515/jgth-2019-0024

Abstract: Abstract Let G be a finite group and, for a prime p, let S be a Sylow p-subgroup of G. A character χ of G is called Sylp{\mathrm{Syl}_{p}}-regular if the restriction of χ to S… read more here.

Keywords: steinberg like; characters finite; like characters; simple groups ... See more keywords