Equation 677 Database

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Magma 90bb9333abe1…

magma 90bb9333abe1
Size
595
Isomorphism class hash
90bb9333abe1c120a695036ef4d925992069152d736ccc207f419a86cf47439e
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 08:51:29
Display reorder
64,42,55,33,10,34,62,43,56,8,32,63,41,54,9,45,52,30,67,13,46,53,31,65,11,44,51,29,66,12,511,512,514,513,510,506,504,509,508,505,503,507,486,487,488,476,477,455,464,234,268,250,269,270,254,240,189,185,186,190,180,181,126,298,297,314,303,319,318,306,386,413,408,410,414,405,406,345,384,382,412,400,409,411,315,307,308,313,302,317,316,159,154,158,127,160,173,188,109,110,114,95,94,113,86,191,192,155,157,128,174,187,68,108,111,115,97,96,112,277,284,283,272,273,271,275,163,117,162,116,164,569,568,588,590,592,593,587,589,591,529,536,515,516,537,544,521,57,78,106,61,24,82,0,93,88,107,105,104,40,7,463,465,470,484,467,459,472,454,475,474,485,483,482,462,228,207,236,245,265,239,219,167,119,178,171,184,182,183,450,451,448,447,449,453,452,312,310,309,299,301,311,300,165,134,153,152,166,144,118,279,278,282,280,281,274,276,266,238,206,227,226,218,193,247,258,251,267,264,263,235,394,407,385,352,380,379,392,393,330,390,331,391,576,577,534,538,549,579,530,546,578,582,585,583,584,581,586,580,495,491,496,493,502,498,490,471,469,456,480,478,460,473,229,237,214,241,225,257,243,16,79,72,18,101,98,25,47,85,58,22,71,39,92,244,209,246,242,212,262,261,492,494,500,489,501,499,497,457,481,479,466,458,468,461,76,84,48,27,77,91,14,80,73,20,102,100,59,23,70,38,83,49,26,90,15,75,81,74,19,103,99,60,324,329,327,332,328,325,326,35,151,222,150,36,575,574,566,526,525,519,520,524,567,531,572,522,533,527,523,573,28,89,6,87,3,4,5,202,249,233,255,198,208,215,140,148,176,131,169,124,125,130,129,168,156,177,121,135,141,142,149,175,132,170,123,200,203,201,248,232,256,197,355,367,368,349,341,346,395,438,444,421,434,442,424,441,344,370,365,353,343,342,348,347,396,383,403,337,376,401,289,304,294,293,290,287,288,422,423,440,437,443,420,433,402,350,397,369,366,354,416,321,417,415,418,320,545,542,528,557,532,555,550,558,556,539,554,540,547,553,548,594,50,1,17,37,2,69,21,213,221,217,205,260,220,253,336,381,333,359,378,340,387,361,364,375,371,351,404,372,196,252,230,194,210,224,199,161,136,139,146,143,133,179,145,120,172,137,122,138,147,216,204,259,231,195,211,223,388,398,334,374,389,338,363,427,431,429,425,445,435,419,360,377,399,335,373,339,362,439,428,432,430,426,446,436,285,292,296,305,286,295,291,357,323,358,322,356,552,551,563,559,561,560,564,562,565,518,570,517,541,535,543,571 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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#a8026a02368cc98eace7a76910bb242dec082e21ec6371f1fc7226b87fb07666, M = the submagma generated by {1, 10} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-06 08:51:30 · history