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898
A Study of Subgroup Discovery Approaches for Defect Prediction
"... Context: Although many papers have been published on software defect prediction techniques, machine learning approaches have yet to be fully explored. Objective: In this paper we suggest using a descriptive approach for defect prediction rather than the precise classification techniques that are usu ..."
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that are usually adopted. This allows us to characterise defective modules with simple rules that can easily be applied by practitioners and deliver a practical (or engineering) approach rather than a highly accurate result. Method: We describe two wellknown subgroup discovery algorithms, the SD algorithm
The McKay correspondence as an equivalence of derived categories
 J. AMER. MATH. SOC
, 2001
"... The classical McKay correspondence relates representations of a finite subgroup G SL(2;C) to the cohomology of the wellknown minimal resolution of the Kleinian singularity C2=G. GonzalezSprinberg and Verdier [10] interpreted the McKay correspondence as an isomorphism on K theory, observing that t ..."
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Cited by 235 (7 self)
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The classical McKay correspondence relates representations of a finite subgroup G SL(2;C) to the cohomology of the wellknown minimal resolution of the Kleinian singularity C2=G. GonzalezSprinberg and Verdier [10] interpreted the McKay correspondence as an isomorphism on K theory, observing
Parabolic subgroups of Garside groups
, 2008
"... A Garside monoid is a cancellative monoid with a finite lattice generating set; a Garside group is the group of fractions of a Garside monoid. The family of Garside groups contains the ArtinTits groups of spherical type. We generalise the wellknown notion of a parabolic subgroup of an ArtinTits g ..."
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Cited by 8 (3 self)
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A Garside monoid is a cancellative monoid with a finite lattice generating set; a Garside group is the group of fractions of a Garside monoid. The family of Garside groups contains the ArtinTits groups of spherical type. We generalise the wellknown notion of a parabolic subgroup of an Artin
ON NORMAL SUBGROUPS OF PRODUCT OF GROUPS
, 2005
"... Abstract. The object of this paper is to find a necessary and sufficient condition for the groups G1, G2,..., Gn so that every normal subgroup of the product ∏n i=1 Gi is of the type ∏n i=1 Ni with Ni � Gi, i = 1, 2,...,n. As a consequence we obtain a wellknown result due to R. Remak about centrele ..."
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Abstract. The object of this paper is to find a necessary and sufficient condition for the groups G1, G2,..., Gn so that every normal subgroup of the product ∏n i=1 Gi is of the type ∏n i=1 Ni with Ni � Gi, i = 1, 2,...,n. As a consequence we obtain a wellknown result due to R. Remak about
subgroups of groups with nontrivial Floyd boundary
 Comm. Algebra
, 2003
"... Abstract. We prove that when a countable group admits a nontrivial Floydtype boundary, then every nonelementary and metrically proper subgroup contains a noncommutative free subgroup. This generalizes the corresponding wellknown results for hyperbolic groups and groups with infinitely many ends. I ..."
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Cited by 19 (3 self)
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Abstract. We prove that when a countable group admits a nontrivial Floydtype boundary, then every nonelementary and metrically proper subgroup contains a noncommutative free subgroup. This generalizes the corresponding wellknown results for hyperbolic groups and groups with infinitely many ends
Stability in the homology of congruence subgroups
 Invent. Math
"... The homology groups of many natural sequences of groups fGng¥n=1 (e.g. general linear groups, mapping class groups, etc.) stabilize as n! ¥. Indeed, there is a wellknown machine for proving such results that goes back to early work of Quillen. Church and Farb discovered that many sequences of grou ..."
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Cited by 9 (2 self)
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The homology groups of many natural sequences of groups fGng¥n=1 (e.g. general linear groups, mapping class groups, etc.) stabilize as n! ¥. Indeed, there is a wellknown machine for proving such results that goes back to early work of Quillen. Church and Farb discovered that many sequences
Subgroup Discovery for Defect Prediction
"... Although there is extensive literature in software defect prediction techniques, machine learning approaches have yet to be fully explored and in particular, Subgroup Discovery (SD) techniques. SD algorithms aim to find subgroups of data that are statistically different given a property of interest ..."
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Cited by 3 (0 self)
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) for the property of interest and do not necessarily describe all instances in the dataset. In this preliminary study, we have compared two wellknown algorithms, the Subgroup Discovery algorithm [3] and CN2SD algorithm [4], by applying them to several datasets from the publicly available PROMISE repository [5
Hidden Subgroup States are Almost Orthogonal
, 1999
"... It is well known that quantum computers can efficiently find a hidden subgroup H of a finite Abelian group G. This implies that after only a polynomial (in log jGj) number of calls to the oracle function, the states corresponding to different candidate subgroups have exponentially small inner pr ..."
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Cited by 34 (2 self)
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It is well known that quantum computers can efficiently find a hidden subgroup H of a finite Abelian group G. This implies that after only a polynomial (in log jGj) number of calls to the oracle function, the states corresponding to different candidate subgroups have exponentially small inner
THE STABLE HOMOLOGY OF CONGRUENCE SUBGROUPS
"... 0.1. Introduction. Let F be a number field, and let Γ = SLN(OF). For an integer M, let Γ(M) denote the principal congruence subgroup of level M. The cohomology of Γ in any fixed degree is well known to be stable as N → ∞ stable in fixed degree [Cha80]. The cohomology of Γ(M), however, does not stab ..."
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Cited by 4 (2 self)
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0.1. Introduction. Let F be a number field, and let Γ = SLN(OF). For an integer M, let Γ(M) denote the principal congruence subgroup of level M. The cohomology of Γ in any fixed degree is well known to be stable as N → ∞ stable in fixed degree [Cha80]. The cohomology of Γ(M), however, does
On XPermutable Subgroups
, 2012
"... A subgroup A of a group G is said to be Xpermutable with another subgroup B in G, where ∅ 6 = X ⊆ G, if there exists some element x ∈ X such that ABx = BxA. In this paper, the solubility and supersolubility of finite groups are described by Xpermutability of the Hall subgroups and their subgroups ..."
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and their subgroups, in addition, the well known theorem of SchurZassenhaus in finite group is generalized.
Results 1  10
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