Equation 677 Database

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Magma 9c59641c53ac…

magma 9c59641c53ac
Size
381
Isomorphism class hash
9c59641c53ac46bb37e0a0a96e0a8177433ee274b79702214f27e4955ce084f5
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:41:45
Display reorder
380,44,43,45,46,47,42,28,29,24,25,26,27,36,37,38,39,40,41,319,320,321,322,323,318,279,289,299,249,259,269,209,219,229,238,189,199,52,53,48,49,50,51,56,57,58,59,54,55,196,206,216,226,236,186,266,276,286,296,246,256,31,33,34,30,35,32,337,364,336,379,335,368,348,376,338,339,172,171,173,168,169,170,97,98,99,100,101,96,177,178,179,174,175,176,302,303,304,305,301,300,275,285,295,245,255,265,205,215,225,235,185,195,12,13,14,15,16,17,22,23,18,19,20,21,198,208,218,228,239,188,268,278,287,298,248,258,104,106,107,103,102,105,359,367,347,375,346,363,334,378,358,333,69,68,70,71,66,67,86,87,88,89,84,85,65,60,61,62,63,64,326,327,328,329,324,325,277,288,297,247,257,267,207,217,227,237,187,197,72,73,74,75,76,77,82,83,78,79,80,81,192,202,212,222,232,182,262,272,282,292,242,252,90,92,93,95,94,91,340,360,345,377,344,365,343,373,341,342,3,2,4,5,1,0,111,112,113,108,109,110,10,11,6,7,8,9,310,311,306,307,308,309,274,284,294,244,254,264,204,214,224,234,184,194,146,147,148,149,144,145,151,152,153,154,155,150,190,201,211,221,231,180,260,270,280,291,240,250,119,115,116,118,117,114,332,369,349,374,350,362,355,371,331,356,132,137,133,134,135,136,130,131,126,127,128,129,138,139,140,141,142,143,314,315,316,317,312,313,273,283,293,243,253,263,203,213,223,233,183,193,161,156,157,158,159,160,167,162,163,164,165,166,191,200,210,220,230,181,261,271,281,290,241,251,123,125,120,122,121,124,353,366,352,370,351,361,357,372,354,330 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#b66edbbdcc18ab822aeb8c0e517cc0500614bfcd68d760a94b6b8cc01b086dc5, M = {74} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 51.

last edited by qawbecrdtey at 2026-10-01 23:41:46 · history