Equation 677 Database

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Magma eb0c7890b42c…

magma eb0c7890b42c
Size
705
Isomorphism class hash
eb0c7890b42cb737749ab039820936d3326f86b8a8aaeba3677751ce8cfd2551
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 16:45:58
Display reorder
660,104,103,102,106,107,105,101,99,100,97,98,96,639,582,583,640,584,641,585,638,586,636,587,637,580,645,581,646,579,647,576,644,577,642,578,643,504,649,505,650,506,648,507,652,508,653,509,651,510,655,511,656,512,654,513,658,514,659,515,657,661,665,668,679,335,334,333,330,331,332,325,326,324,328,329,327,91,463,464,92,462,90,466,94,467,95,465,93,461,89,459,87,460,88,457,85,458,86,456,84,401,313,399,314,400,312,397,316,398,317,396,315,407,319,405,320,406,318,403,322,404,323,402,321,687,685,686,698,138,140,139,143,141,142,135,136,137,134,132,133,64,603,604,65,605,63,602,60,600,61,601,62,609,70,610,71,611,69,608,66,606,67,607,68,159,541,160,542,161,540,158,544,156,545,157,543,165,547,166,548,167,546,164,550,162,551,163,549,662,666,663,680,46,45,47,44,42,43,36,37,38,39,40,41,471,340,341,472,339,473,336,470,337,468,338,469,346,477,347,478,345,479,342,476,343,474,344,475,7,413,8,411,6,412,10,409,11,410,9,408,5,419,3,417,4,418,0,415,2,416,1,414,673,675,672,689,353,352,351,348,349,350,358,359,357,354,355,356,281,368,366,279,367,280,371,277,369,278,370,276,363,287,364,285,365,286,362,283,360,284,361,282,428,484,426,485,427,483,431,480,429,481,430,482,423,490,424,491,425,489,422,486,420,487,421,488,664,667,669,681,113,112,111,108,109,110,118,119,117,114,115,116,535,527,525,536,526,534,523,538,524,539,522,537,518,533,516,531,517,532,521,529,519,530,520,528,592,121,593,122,591,120,588,124,589,125,590,123,598,127,599,128,597,126,594,130,595,131,596,129,692,694,696,701,213,215,214,211,212,210,206,204,205,209,207,208,236,226,227,234,225,235,222,239,223,237,224,238,217,231,218,232,216,233,220,230,221,228,219,229,246,202,247,203,248,201,249,198,250,199,251,200,244,193,245,194,243,192,240,196,241,197,242,195,699,700,703,704,381,383,382,379,380,378,374,372,373,377,375,376,288,437,435,289,436,290,433,291,434,292,432,293,443,294,441,295,442,296,439,297,440,298,438,299,254,498,252,499,253,500,257,501,255,502,256,503,260,496,258,497,259,495,263,492,261,493,262,494,691,693,695,702,633,635,634,631,632,630,626,624,625,629,627,628,565,12,13,566,14,564,15,568,16,569,17,567,18,571,19,572,20,570,21,574,22,575,23,573,78,188,79,186,80,187,81,191,82,189,83,190,76,183,77,184,75,185,72,182,73,180,74,181,670,676,678,690,272,271,270,274,275,273,269,267,268,265,266,264,27,300,301,28,302,29,303,26,304,24,305,25,306,33,307,34,308,35,309,32,310,30,311,31,391,451,392,452,390,450,394,454,395,455,393,453,389,449,387,447,388,448,385,445,386,446,384,444,671,677,674,688,51,53,52,49,50,48,59,57,58,55,56,54,622,175,176,623,174,621,178,618,179,619,177,620,173,613,171,614,172,612,169,616,170,617,168,615,151,561,152,562,150,563,154,560,155,558,153,559,149,552,147,553,148,554,145,555,146,556,144,557,682,684,683,697 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#3e7f78778326128ca89bcdb69266df7c07c66aee73c2a2e36b24ead92b52079d, 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 16:45:59 · history