Equation 677 Database

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Magma 57fcd33b5f59…

magma 57fcd33b5f59
Size
707
Isomorphism class hash
57fcd33b5f5902886daa71ce4966986d79f4ad1ef04a799782853b196c991cbc
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 20:54:37
Display reorder
169,168,170,171,172,173,706,233,230,228,229,232,231,262,261,263,258,259,260,191,190,186,187,188,189,58,57,59,54,55,56,196,195,197,192,193,194,67,66,68,69,70,71,80,79,81,82,83,78,87,86,88,89,84,85,204,209,205,206,207,208,24,29,25,26,27,28,432,434,433,430,431,429,436,435,437,439,440,438,506,505,504,507,508,509,503,502,501,498,499,500,569,568,570,571,572,573,551,552,550,553,554,555,356,355,354,561,357,560,549,590,589,546,547,548,331,330,332,333,334,335,341,340,339,338,336,337,628,630,629,625,627,645,639,612,640,626,700,664,686,701,704,702,703,698,705,697,3,1,4,5,2,0,138,143,139,140,141,142,126,131,127,128,129,130,115,114,116,117,118,119,236,235,237,238,239,234,288,289,290,291,292,293,39,38,40,41,36,37,105,104,106,107,102,103,49,48,50,51,52,53,92,91,93,94,95,90,385,384,386,383,381,382,510,512,511,513,574,575,524,523,582,583,525,526,457,456,458,461,459,460,585,584,586,587,588,539,567,484,483,482,480,481,329,328,327,326,324,325,451,450,449,448,446,447,345,347,346,344,342,343,372,371,370,491,373,374,635,607,606,622,623,643,616,638,621,633,699,685,684,675,689,690,691,670,688,668,19,22,20,21,18,23,75,74,76,77,72,73,215,214,210,211,212,213,270,275,271,272,273,274,219,218,220,221,216,217,202,201,203,198,199,200,12,17,13,14,15,16,226,225,227,222,223,224,183,182,184,185,180,181,61,60,62,63,64,65,426,428,427,424,425,423,441,443,442,444,445,562,592,556,593,594,557,558,320,322,321,318,319,317,599,596,595,598,559,597,591,306,307,310,308,309,315,314,316,312,313,311,542,540,541,543,544,545,490,489,488,486,487,485,350,349,348,353,351,352,631,609,610,611,608,644,624,641,614,634,694,682,669,674,679,695,678,683,677,676,121,124,122,123,120,125,284,283,285,286,287,282,7,6,8,9,10,11,32,31,33,34,35,30,43,42,44,45,46,47,98,97,99,100,101,96,132,137,133,134,135,136,250,249,251,246,247,248,240,245,241,242,243,244,113,112,108,109,110,111,363,362,361,358,359,360,364,366,365,367,368,369,494,493,492,495,496,497,377,376,375,378,379,380,581,580,579,323,563,564,578,522,521,520,518,519,514,516,515,576,517,577,566,455,565,454,452,453,527,528,529,530,531,532,538,535,537,536,533,534,619,617,618,620,613,642,637,615,636,632,696,665,672,681,693,687,673,680,692,671,155,152,150,151,154,153,159,158,160,161,156,157,145,144,146,147,148,149,296,294,297,298,299,295,179,178,174,175,176,177,167,166,162,163,164,165,278,277,279,280,281,276,267,266,268,269,264,265,305,304,301,300,302,303,253,252,254,255,256,257,410,409,408,405,406,407,601,602,600,603,604,605,420,422,421,418,419,417,477,479,478,475,476,474,472,471,473,468,469,470,399,401,400,402,403,404,465,467,466,462,463,464,390,392,391,387,388,389,398,397,396,394,395,393,415,414,416,412,413,411,646,655,647,652,651,649,648,654,650,653,667,656,657,661,662,666,660,659,663,658 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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#d668bf04c36f8b4c67728650c5c82a046d470936a3c130394e60cdea0aa42f4e, M = {24, 25, 26, 27, 28, 29, 136} 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, 140): MacNeish's product over GF(4) x GF(5) x GF(7); 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: 101.

last edited by qawbecrdtey at 2026-10-08 20:54:38 · history