Equation 677 Database

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Magma 879f4c2c86c1…

magma 879f4c2c86c1
Size
705
Isomorphism class hash
879f4c2c86c190824e010fadc5268252e12291e9e4f39d0cee57758a92cf9932
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 17:38:12
Display reorder
660,274,354,360,528,338,339,355,275,361,529,353,340,276,359,527,341,273,350,356,524,271,342,351,357,525,343,272,352,358,526,366,336,280,345,534,337,281,346,367,535,335,282,344,365,533,279,332,348,362,530,277,333,349,363,531,278,334,347,364,532,674,683,673,685,49,492,150,402,378,379,493,50,148,403,491,377,51,149,401,374,52,488,146,398,53,375,489,147,399,376,54,490,145,400,141,384,55,498,408,385,56,499,139,409,383,57,497,140,407,58,380,494,144,404,59,381,495,142,405,60,382,496,143,406,670,663,662,666,103,480,390,456,504,505,481,104,391,457,479,503,105,389,455,500,106,476,386,452,107,501,477,387,453,502,108,478,388,454,396,510,101,486,462,511,102,487,397,463,509,100,485,395,461,97,506,482,392,458,98,507,483,393,459,99,508,484,394,460,675,679,682,681,32,540,122,450,234,232,541,33,123,451,539,233,31,121,449,230,35,536,125,446,36,231,537,126,447,229,34,538,124,448,645,644,30,649,648,653,28,657,652,656,636,29,641,637,640,26,613,615,616,617,27,620,625,621,624,25,628,633,629,632,698,700,703,704,254,311,414,284,306,304,312,255,415,285,310,305,253,413,283,302,257,307,410,287,258,303,308,411,288,301,256,309,412,286,420,297,252,317,290,295,250,318,421,291,296,251,316,419,289,248,300,313,416,293,249,298,314,417,294,247,299,315,418,292,691,689,694,690,116,75,546,564,70,71,73,117,547,565,74,72,115,545,563,69,119,78,542,560,120,67,76,543,561,68,118,77,544,562,552,61,114,81,570,62,112,79,553,571,63,113,80,551,569,110,64,84,548,566,111,65,82,549,567,109,66,83,550,568,669,671,664,661,92,202,596,597,198,196,203,93,598,599,204,197,91,595,594,194,95,201,319,1,96,195,199,591,590,193,94,200,593,592,608,189,90,208,609,187,88,209,610,611,188,89,210,607,606,86,192,207,601,600,87,190,205,602,603,85,191,206,604,605,696,695,693,692,9,582,426,438,329,330,583,7,427,439,581,331,8,425,437,328,12,578,422,434,10,326,579,423,435,327,11,580,424,436,432,320,4,588,444,321,5,589,433,445,322,6,587,431,443,3,323,584,428,440,0,324,585,429,441,2,325,586,430,442,677,678,684,687,220,576,372,225,557,558,577,221,373,223,575,559,222,371,224,556,219,572,368,228,217,554,573,369,226,555,218,574,370,227,647,650,211,651,646,658,212,659,655,654,642,213,643,639,638,214,618,619,614,612,215,626,627,623,622,216,634,635,631,630,697,699,701,702,16,516,128,46,242,243,517,17,129,47,515,241,18,127,48,245,15,512,131,45,13,246,513,132,43,244,14,514,130,44,134,240,22,522,37,238,23,523,135,38,239,24,521,133,39,21,236,518,137,40,19,237,519,138,41,20,235,520,136,42,668,672,665,667,259,468,160,163,185,186,469,260,161,164,467,184,261,162,165,181,262,464,159,166,263,182,465,157,167,183,264,466,158,168,151,176,265,474,169,177,266,475,152,170,175,267,473,153,171,268,179,470,154,172,269,180,471,155,173,270,178,472,156,174,686,676,688,680 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#5b838974e03a318bd69da9937fbfbee1bd56d732e0aad8a944a467873e322378, 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 17:38:19 · history