Equation 677 Database

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Magma 87215e667957…

magma 87215e667957
Size
705
Isomorphism class hash
87215e66795797d58ae0c27426bd9b7c53866a6a8bc911091767c5202a2b70cf
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 20:41:34
Display reorder
660,214,19,51,176,503,215,20,52,174,501,213,18,53,175,502,22,210,50,179,499,23,211,48,177,500,21,212,49,178,498,57,17,171,205,494,58,15,172,206,492,59,16,173,204,493,13,56,170,208,497,14,54,168,209,495,12,55,169,207,496,668,666,664,670,367,563,252,242,47,368,561,253,240,45,366,562,254,241,46,559,370,255,245,43,560,371,256,243,44,558,369,257,244,42,258,554,248,365,38,259,552,246,363,36,260,553,247,364,37,557,261,251,361,41,555,262,249,362,39,556,263,250,360,40,686,690,688,685,201,632,491,599,455,202,630,489,597,453,203,631,490,598,454,628,200,487,595,451,629,198,488,596,452,627,199,486,594,450,482,623,590,192,446,480,621,588,193,444,481,622,589,194,445,626,485,593,195,449,624,483,591,196,447,625,484,592,197,448,665,663,672,671,274,419,527,383,406,275,417,525,381,407,273,418,526,382,405,415,270,523,379,402,416,271,524,380,403,414,272,522,378,404,518,410,374,265,397,516,408,372,266,398,517,409,373,264,396,413,521,377,268,400,411,519,375,269,401,412,520,376,267,399,681,673,678,676,108,515,575,431,277,109,513,573,429,278,110,514,574,430,276,511,111,571,427,280,512,112,572,428,281,510,113,570,426,279,566,506,422,114,283,564,504,420,115,284,565,505,421,116,282,509,569,425,117,286,507,567,423,118,287,508,568,424,119,285,669,661,667,662,35,551,190,467,5,33,549,191,465,3,34,550,189,466,4,547,31,186,463,0,548,32,187,464,2,546,30,188,462,1,181,542,458,26,11,182,540,456,24,9,180,541,457,25,10,545,184,461,29,7,543,185,459,27,8,544,183,460,28,6,696,693,697,694,106,659,656,657,658,107,651,650,648,649,105,655,652,653,654,640,102,606,84,93,641,103,607,85,94,639,104,608,86,95,601,635,79,97,88,602,633,80,98,89,600,634,78,96,87,638,604,82,100,91,636,605,83,101,92,637,603,81,99,90,701,703,704,702,296,222,646,125,647,294,223,642,123,643,295,224,645,124,644,225,299,139,121,141,226,297,140,122,142,227,298,138,120,143,134,220,131,291,64,132,221,129,292,65,133,219,130,293,63,216,137,127,290,60,217,135,128,288,61,218,136,126,289,62,700,699,698,695,157,395,359,539,323,158,393,357,537,321,156,394,358,538,322,391,160,355,535,319,392,161,356,536,320,390,159,354,534,318,350,386,530,163,314,348,384,528,164,312,349,385,529,162,313,389,353,533,166,317,387,351,531,167,315,388,352,532,165,316,675,674,677,682,235,587,479,443,620,236,585,477,441,618,234,586,478,442,619,583,238,475,439,616,584,239,476,440,617,582,237,474,438,615,470,578,434,233,611,468,576,432,231,609,469,577,433,232,610,581,473,437,229,614,579,471,435,230,612,580,472,436,228,613,680,684,683,679,304,345,76,148,330,305,346,77,149,331,303,347,75,147,332,344,300,72,144,333,342,301,73,145,334,343,302,74,146,335,67,336,154,310,328,68,337,155,311,329,66,338,153,309,327,339,70,150,306,324,340,71,151,307,325,341,69,152,308,326,689,687,692,691 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#cb899e6f30effddffe30366e2e9dc963aa0ce854a3a9ff04422e3e195000d2a8, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 20:41:35 · history