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Indecomposable S6(2, 3, v)'s

1991
*
Journal of combinatorial theory. Series A
*

In this paper, we determine the spectrum for

doi:10.1016/0097-3165(91)90019-d
fatcat:x7ghllksjva2lcdtfs2yr5p4qe
*indecomposable**S*,(*2*,*3*, u))*s*, and we prove the existence of MPT-free Ss(*2*,*3*,*v*) for all*v*> 9 and u = 7. 0 1991 Academic Press, Inc. ... Let now u*2*17. If (u -1)/*2*= 0 (mod*2*), Lemma 4.4 gives a simple and MPT-free*S*, (*2*,*3*, u). ... If (u -1)/*2*E 1 (mod*2*), since there exists a simple and MPT-free*S6*(*2*,*3*, u) for u = 23, 5 + 12k, k > 1, Lemma 4.5, by induction, gives a simple and MPT-free F& (*2*,*3*, u). ...##
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The new stems (πS N, 46≤N≤64)
[chapter]

1990
*
Lecture notes in mathematics
*

(a) o'2A[32,1] ~ A[32,1] = u c

doi:10.1007/bfb0083802
fatcat:cxpc455u6nfxpi5tsdjij4rvge
*v*'~*S*= 0. 43 (b) Since A[39,3] ~ , ~A[39,3] e ~ = <~,u,B[34]>n = <~,*v*,>n D <~,u,n,*2*>nA[32,1] = 0 because*S*<¢,*v*,w,*2*> e ~13 = O. ...*S*while the other elements of ~ are divisible by n and thus have order two.) 46 Now "~<*2*, A[40,1],*v*> = <'~,*2*,A[40,1]>*v*= O. Thus, <*2*,A[40,1],*v*> = 2kC[44]. ... [7.41] Now 2A[62,2] •*2*<A[*S6*],*2*,n,*v*> c <<*2*,A[*S6*],*2*>,n,*v*> c <nA[*S6*],n,u> = <vA[S4,1],n,*v*> D A[S4,1]<*v*,n,*v*> = A[8]A[54,1] = <n,*v*,2v>A[54,1] = n<*v*,2u,A[54,1]>. ...##
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Certain representation algebras

1965
*
Journal of the Australian Mathematical Society
*

We have the following P r o p o

doi:10.1017/s1446788700025908
fatcat:eo243ccvg5bmjbwqua2i4uumfq
*s*i t i o n*3*. The projective ideal 2i is semi-simple and finite dimen sional. R e m a r k . ... In these cases there are only a finite number of different*indecomposable*classes and so sé is a direct sum of copies of . ... * 1 splits up into*3**indecomposable*, non-isomorphic 1F(S4 i)-modules £C A (all superscripts will be considered to be in tegers modulo*3*), such that (^a )^4 ^**S6*', as in proposition*3*of [*2*] . ...##
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Vertices and sources

1967
*
Journal of Algebra
*

For each ring

doi:10.1016/0021-8693(67)90009-9
fatcat:xdfa74pdinhtrfky5gxrcllpze
*S*and group 6,*S6*is the group ring of 6 over*S*. If*S*is a subring of*S*' and g is a subgroup of @, we view Sg as a subring of*S*'6. ... Since L is*indecomposable*it follows from Lemma 1 that no component of L -.is projective. Since (Ms,) '*v*A& , it follows from the*indecomposability*of*S*that 1 !x*S*. LEMMA 4. ...##
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On the indecomposability of induced modules

1986
*
Journal of Algebra
*

Condition (i) is then just that

doi:10.1016/0021-8693(86)90214-0
fatcat:copk6wgavzcodmeysgb64kf7qm
*S*is*indecomposable*, while (ii) asserts that HZ TJS). If R is a field, the theorem is therefore precisely Theorem 9.6(a), (c) in [*3*, Chap. VII]. ... Then*v*is*indecomposable*for every*indecomposable*direct summand W of SH. Moreover, if W, and W2 are two surh .summands, then WY z WF if and only 17 W, E W,. Remarks. ... Why some condition is needed here will become clear in the proof. (*3*) In case R = 0 or R = F, Green's*Indecomposability*Theorem asserts that SN is*indecomposable*provided*S*is and O"(N)*s*U. ...##
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Concealed-Canonical Algebras and Separating Tubular Families

1999
*
Proceedings of the London Mathematical Society
*

(

doi:10.1112/s0024611599001872
fatcat:e7vjkmylp5d5nhmocxsuwunjx4
*v*) For 1 < i < t there are short exact sequences 0*3*L « f i*3*L i 1*3*t À1*S*i*3*0; 0*3*L i 1*3*L i*2**3*t À2*S*i*3*0; . . . 0*3*L i p i À*2**3*L i p i À 1*3*t À p i À 1*S*i*3*0; 0*3*L «*3*L*3**S**3*0; 0 ... By the dual of (S16) we get a connecting sequence h: 0*3*N*3**V*x*3*N*3*0 with*V*x P U x and N P mod*S*. ... translation for H; (*v*) H admits*S*and the corresponding canonical algebra L as torsion-free ...##
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Classification of stable homotopy types with torsion-free homology

2001
*
Topology
*

We compute the number of

doi:10.1016/s0040-9383(99)00084-1
fatcat:m7uly3id2jgaratl2p3ohaopl4
*indecomposable*stable homotopy types with "nitely generated torsion free homology of stable dimension k*0. ... We de"ne the spaces > G and >T H with i3+1,*2*,5,, j3+1,2,3,, v3+1,*2*,6, by > "*S*"X(*S*), > "*S6*E e"X( ) , > "*S6*E e"X( ) , > "*S*"X(*S*), > "*S*"X(*S*), >T "X(*v*) , >T "X(*v*) , >T "X(*v*) . ... Indeed, the ring consists of the matrices of the same form as in for which rows and columns only correspond, however, to the indexes i"1,*2*,*3*, 4, 5 and the pairs (*v*, j) with*v*"*3*, 6 and j"1,*2*,*3*. ...##
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Algebras stably equivalent to Nakayama algebras of Loewy length at most 4

1979
*
Journal of the Australian Mathematical Society
*

Idun Reiten [

doi:10.1017/s1446788700016621
fatcat:pczzd4dcn5bqdl3pgslyihx7ue
*2*] of use, available at https://www.cambridge.org/core/terms. https://doi. ... ( T \ I ' )*V*-'i+i/ IT \ i i + 1 \ so that t + l W*S*i +*2*). ... Hence (T \ i*\ (T \ we must have ( J^W*S*j l and ( 4 )<-+*S*5 . It further follows that T 6^*S6*and l Ss \ W (e) Assume that P*3*has length*3*. We must then have If T A^TU P^P X is not uniserial. ...##
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On saturated fusion systems and Brauer indecomposability of Scott modules
[article]

2010
*
arXiv
*
pre-print

So,M = Ind

arXiv:1009.2391v1
fatcat:llx247sxzvbmlkvi35cayztj4i
*S6*S5 (O). Now, if u = (1,*3*), then χ(u) = 4 and if u = (1,*2*)(*3*, 4) or u = (1,*2*,*3*, 4) then χ(u) =*2*. ... Case: P = (1,*2*,*3*, 4), (1,*3*)(5, 6) . The image of P under the exceptional noninner automorphism of*S*6 is*S*6 -conjugate to (1,*2*,*3*, 4) , (1,*3*) . ...##
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A complete classification of homogeneous plane continua
[article]

2016
*
arXiv
*
pre-print

The main technical result in this paper is a new characterization of the pseudo-arc: a non-degenerate continuum is homeomorphic to the pseudo-arc if and only if it is hereditarily

arXiv:1409.6324v2
fatcat:6r2kev4btza5rbmcar4irz4pva
*indecomposable*and has ... Moreover, by (*S6*) for*S*and since ϕ(F 1 ∪ F*2*) = π(P 1 ∪ P*2*), we have that ϕ −1 (α i0 ) ⊂ (F*3*) , so that ϕ −1 (α i0 ) ∩ (F*3*) = ϕ −1 (α i0 ) = α i0 . Thus E(*S*i0 ) = α i0 ∪ β i0 . ... ⊂*V*, X*2*∩ X*3*⊂ U , and X 1 ∩ X*3*= ∅. ...##
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Subcontinua with degenerate tranches in hereditarily decomposable continua

1983
*
Transactions of the American Mathematical Society
*

*S*. Thomas, Jr. Theorem. Every hereditarily decomposable continuum contains a subcontinuum with a degenerate tranche. Corollary. ... Let (U,

*V*) be a subcollection of A such that (l)U,VC(U,

*V*), (

*2*) (U,

*V*) is a cover of some subcontinuum K of M such that U n K =£ 0 ¥=

*V*n K, and (

*3*) if W C (U,

*V*) is a cover of a subcontinuum L of M such ... Then Cl(U/T) C U/

*S*n UR.To see this, let W E fT. There exists Z E C\F such that ZniF^0. Let FE/1 such that

*S*\Z,C) C

*V*. Since C1(Z) C F, F <

*2*

*S*. Let F"...,F" E

*S*such that Cl(FF) C F, U • • • U

*V*". ...

##
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Subcontinua with Degenerate Tranches in Hereditarily Decomposable Continua

1983
*
Transactions of the American Mathematical Society
*

*S*. Thomas, Jr. Theorem. Every hereditarily decomposable continuum contains a subcontinuum with a degenerate tranche. Corollary. ... Let (U,

*V*) be a subcollection of A such that (l)U,VC(U,

*V*), (

*2*) (U,

*V*) is a cover of some subcontinuum K of M such that U n K =£ 0 ¥=

*V*n K, and (

*3*) if W C (U,

*V*) is a cover of a subcontinuum L of M such ... Then Cl(U/T) C U/

*S*n UR.To see this, let W E fT. There exists Z E C\F such that ZniF^0. Let FE/1 such that

*S*\Z,C) C

*V*. Since C1(Z) C F, F <

*2*

*S*. Let F"...,F" E

*S*such that Cl(FF) C F, U • • • U

*V*". ...

##
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Generating large indecomposable continua

1976
*
Pacific Journal of Mathematics
*

Bellamy that every metric continuum is homeomorphic to a retract of some metric

doi:10.2140/pjm.1976.62.587
fatcat:2gq635sr7vh3nhtcq7jln6b3vm
*indecomposable*continuum. This result was later extended by G. R. ... Suppose*S**2*and*S**2*are two distinct subsets of a and a is an element of Si not in*S**2*. ... From condition (*2*) it follows that I a C*V*, so I a C*V*=*V*-/ α Π VCM-/ α . Now suppose M is the union of two proper subcontinua H and K. ...##
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Morita equivalence for semigroups

1995
*
Journal of the Australian Mathematical Society
*

The conditions (

doi:10.1017/s1446788700038489
fatcat:tdnushfggrdvbgxdnsv3h47oau
*2*), (*3*) and (4) follow from the fact that for a monoid R and aleft/?-actM, R® R M = M. Since*S*is a monoid, it is an*indecomposable*projective left*S*-act. ... T h e n either (*s*, t • <i>) = (M,*v*• r)), in which case*s*® t ® = u<g>*v*-r)inS<8) 5Hom(f/, N), or for some n >*2*there exists a sequence, (5, *•<! ... Formally, let d*2*), (a,ba), (b,ab), (b,bc), (c,cb), (c,dc) , (d, cd) , (d, da)}, let A be the congruence generated by A o on the free semigroup F x and let*S*P4 = F x /A. ...##
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Blocks with a cyclic defect group

1975
*
Journal of Algebra
*

Now for the Green correspondence (m, ,

doi:10.1016/0021-8693(75)90181-7
fatcat:lpbdgvhtendgfo4ln3x3lcqgju
*2*,) + (m, B) notice that the set*3*= {D n D: x E Nt\rn} = {l}, and hence 41 = {*S*: 1 <*S*< D). ... Moreover there exists a permutation 8 of I so that the "socle" E(f Vi)*s**S6*-lti) for all i E I. ...
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