Equation 677 Database

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Magma 79cfdf2f4769…

magma 79cfdf2f4769
Size
705
Isomorphism class hash
79cfdf2f476986d6d00425b7b8f5f241d3b3e52a638258287d009497241a292a
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 17:25:44
Display reorder
660,383,555,68,531,359,384,556,69,532,360,385,557,70,533,361,382,554,71,530,358,380,552,72,528,356,381,553,73,529,357,74,389,561,537,365,75,390,562,538,366,76,391,563,539,367,388,77,560,536,364,386,78,558,534,362,387,79,559,535,363,685,677,676,684,331,499,263,347,229,329,500,264,348,227,330,501,265,349,228,327,498,262,346,225,328,496,260,344,226,326,497,261,345,224,269,322,505,353,235,270,320,506,354,233,271,321,507,355,234,325,268,504,352,231,323,266,502,350,232,324,267,503,351,230,668,662,669,664,34,463,132,335,487,32,464,133,336,488,33,465,131,337,489,37,462,128,334,486,35,460,129,332,484,36,461,130,333,485,138,40,469,341,493,139,38,470,342,494,137,39,471,343,495,43,134,468,340,492,41,135,466,338,490,42,136,467,339,491,680,674,682,673,511,567,239,455,18,512,568,240,456,19,513,569,241,457,17,510,566,238,454,14,508,564,236,452,15,509,565,237,453,16,245,641,642,640,636,246,649,650,648,645,247,657,658,656,653,630,244,631,633,632,514,242,570,458,13,515,243,571,459,12,704,700,703,699,371,543,289,395,519,372,544,287,396,520,373,545,288,397,521,370,542,285,394,518,368,540,286,392,516,369,541,284,393,517,295,377,549,401,525,293,378,550,402,526,294,379,551,403,527,376,291,548,400,524,374,292,546,398,522,375,290,547,399,523,693,690,692,691,102,599,89,407,443,103,600,90,408,444,101,601,91,409,445,98,598,88,406,442,99,596,86,404,440,100,597,87,405,441,80,93,605,413,449,81,94,606,414,450,82,92,607,415,451,96,83,604,412,448,97,84,602,410,446,95,85,603,411,447,672,661,667,666,191,175,47,186,163,192,173,48,187,161,193,174,49,185,162,190,171,46,182,159,188,172,44,183,160,189,170,45,184,158,53,197,166,177,154,54,198,164,178,152,55,199,165,176,153,196,52,169,180,157,194,50,167,181,155,195,51,168,179,156,695,689,696,694,619,431,110,140,27,620,432,111,141,28,621,433,112,142,26,618,430,113,143,30,616,428,114,144,31,617,429,115,145,29,108,625,437,146,25,109,626,438,147,23,107,627,439,148,24,624,104,436,149,21,622,105,434,150,22,623,106,435,151,20,679,688,683,675,611,203,60,210,216,612,204,61,208,214,613,202,62,209,215,610,206,66,213,219,608,207,59,211,217,609,205,65,212,218,63,643,637,638,639,64,651,644,646,647,67,659,652,654,655,635,56,634,629,628,614,57,201,222,220,615,58,200,223,221,698,702,697,701,278,311,252,587,300,279,312,253,588,301,280,313,251,589,299,281,310,248,586,296,282,308,249,584,297,283,309,250,585,298,258,276,317,593,306,259,277,318,594,307,257,275,319,595,305,272,254,316,592,302,273,255,314,590,303,274,256,315,591,304,663,670,665,671,575,475,126,419,4,576,476,127,420,5,577,477,125,421,3,574,474,122,418,1,572,472,123,416,0,573,473,124,417,2,117,581,481,425,10,118,582,482,426,11,116,583,483,427,9,580,120,480,424,6,578,121,478,422,7,579,119,479,423,8,681,686,687,678 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#555d8536a50144822bfea9b20f3ef68710f5792b887e6dda4840627962426043, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 17:25:47 · history