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Indecomposable S6(2, 3, v)'s

Salvatore Milici
1991 Journal of combinatorial theory. Series A  
In this paper, we determine the spectrum for 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).  ... 
doi:10.1016/0097-3165(91)90019-d fatcat:x7ghllksjva2lcdtfs2yr5p4qe

The new stems (πS N, 46≤N≤64) [chapter]

Stanley O. Kochman
1990 Lecture notes in mathematics  
(a) o'2A[32,1] ~ A[32,1] = u c 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]>.  ... 
doi:10.1007/bfb0083802 fatcat:cxpc455u6nfxpi5tsdjij4rvge

Certain representation algebras

S. B. Conlon
1965 Journal of the Australian Mathematical Society  
We have the following P r o p o 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] .  ... 
doi:10.1017/s1446788700025908 fatcat:eo243ccvg5bmjbwqua2i4uumfq

Vertices and sources

John G Thompson
1967 Journal of Algebra  
For each ring 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.  ... 
doi:10.1016/0021-8693(67)90009-9 fatcat:xdfa74pdinhtrfky5gxrcllpze

On the indecomposability of induced modules

Reinhard Knörr
1986 Journal of Algebra  
Condition (i) is then just that 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.  ... 
doi:10.1016/0021-8693(86)90214-0 fatcat:copk6wgavzcodmeysgb64kf7qm

Concealed-Canonical Algebras and Separating Tubular Families

Helmut Lenzing, José Antonio De La Peña
1999 Proceedings of the London Mathematical Society  
(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  ... 
doi:10.1112/s0024611599001872 fatcat:e7vjkmylp5d5nhmocxsuwunjx4

Classification of stable homotopy types with torsion-free homology

Hans-Joachim Baues, Yuri Drozd
2001 Topology  
We compute the number of 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.  ... 
doi:10.1016/s0040-9383(99)00084-1 fatcat:m7uly3id2jgaratl2p3ohaopl4

Algebras stably equivalent to Nakayama algebras of Loewy length at most 4

Idun Reiten
1979 Journal of the Australian Mathematical Society  
Idun Reiten [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.  ... 
doi:10.1017/s1446788700016621 fatcat:pczzd4dcn5bqdl3pgslyihx7ue

On saturated fusion systems and Brauer indecomposability of Scott modules [article]

Radha Kessar, Naoko Kunugi, Naofumi Mitsuhashi
2010 arXiv   pre-print
So,M = Ind 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) .  ... 
arXiv:1009.2391v1 fatcat:llx247sxzvbmlkvi35cayztj4i

A complete classification of homogeneous plane continua [article]

L. C. Hoehn, L. G. Oversteegen
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 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 = ∅.  ... 
arXiv:1409.6324v2 fatcat:6r2kev4btza5rbmcar4irz4pva

Subcontinua with degenerate tranches in hereditarily decomposable continua

Lex G. Oversteegen, E. D. Tymchatyn
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".  ... 
doi:10.1090/s0002-9947-1983-0701520-7 fatcat:dllzzpoqgzbh7lpvokkys3742a

Subcontinua with Degenerate Tranches in Hereditarily Decomposable Continua

Lex G. Oversteegen, E. D. Tymchatyn
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".  ... 
doi:10.2307/1999180 fatcat:qc7tx5yhpjeafdqqwhj55tykku

Generating large indecomposable continua

Michel Smith
1976 Pacific Journal of Mathematics  
Bellamy that every metric continuum is homeomorphic to a retract of some metric 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.  ... 
doi:10.2140/pjm.1976.62.587 fatcat:2gq635sr7vh3nhtcq7jln6b3vm

Morita equivalence for semigroups

S. Talwar
1995 Journal of the Australian Mathematical Society  
The conditions (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.  ... 
doi:10.1017/s1446788700038489 fatcat:tdnushfggrdvbgxdnsv3h47oau

Blocks with a cyclic defect group

R.M Peacock
1975 Journal of Algebra  
Now for the Green correspondence (m, , 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.  ... 
doi:10.1016/0021-8693(75)90181-7 fatcat:lpbdgvhtendgfo4ln3x3lcqgju
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