Equation 677 Database

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Magma 4888747a2ea9…

magma 4888747a2ea9
Size
705
Isomorphism class hash
4888747a2ea9026c5b5d04bfc65804e79904611ba4291d86027852ca31a84217
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 15:18:46
Display reorder
660,163,191,249,188,175,250,164,186,176,189,251,190,162,187,174,159,252,194,184,171,160,253,192,185,172,161,254,193,183,173,154,255,197,179,166,155,256,195,177,167,153,257,196,178,165,258,157,200,182,169,259,158,198,180,170,260,156,199,181,168,666,662,661,672,345,340,51,304,399,52,346,305,400,341,50,339,347,303,401,348,54,343,307,402,349,55,344,308,403,350,53,342,306,404,351,57,338,302,397,352,58,336,300,398,353,56,337,301,396,60,354,334,298,393,61,355,335,299,394,59,356,333,297,395,690,686,685,687,217,209,110,471,387,108,218,472,388,207,109,208,216,473,389,213,106,212,474,390,214,107,210,475,391,215,105,211,476,392,223,116,204,469,385,224,114,205,470,386,222,115,206,468,384,112,219,203,465,381,113,220,201,466,382,111,221,202,467,383,667,663,665,668,133,435,314,363,151,312,134,364,152,436,313,437,132,365,150,129,310,438,366,147,130,311,439,367,148,131,309,440,368,149,139,320,433,361,142,140,318,434,362,143,138,319,432,360,141,316,135,429,357,145,317,136,430,358,146,315,137,431,359,144,674,678,673,677,423,507,326,519,85,324,424,520,83,508,325,509,425,521,84,426,322,510,522,81,427,323,511,523,82,428,321,512,524,80,421,332,505,517,76,422,330,506,518,74,420,331,504,516,75,328,417,501,513,79,329,418,502,514,77,327,419,503,515,78,670,671,664,669,459,447,38,495,269,39,460,496,267,448,40,449,461,497,268,462,41,450,498,272,463,42,451,499,270,464,43,452,500,271,457,44,445,493,264,458,45,446,494,265,456,46,444,492,266,47,453,441,489,263,48,454,442,490,261,49,455,443,491,262,696,697,695,694,1,7,124,586,629,125,642,643,640,641,123,647,644,645,646,648,127,651,649,650,652,128,655,653,654,656,126,659,657,658,2,122,8,584,624,3,120,9,585,625,0,121,10,583,623,118,5,11,580,627,119,6,12,581,628,117,4,13,582,626,701,702,703,704,605,275,103,86,561,104,606,630,631,273,102,274,607,633,632,608,99,278,635,634,609,100,276,637,636,610,101,277,639,638,603,94,281,91,567,604,95,279,92,565,602,93,280,90,566,97,599,284,87,563,98,600,282,88,564,96,601,283,89,562,699,700,698,693,26,411,247,593,483,248,27,594,484,412,246,413,28,595,485,29,243,414,596,486,30,244,415,597,487,31,245,416,598,488,32,238,409,591,481,33,239,410,592,482,34,237,408,590,480,241,35,405,587,477,242,36,406,588,478,240,37,407,589,479,682,679,684,676,543,574,286,617,375,287,544,618,376,575,285,576,545,619,377,546,289,577,620,378,547,290,578,621,379,548,288,579,622,380,541,292,572,615,373,542,293,573,616,374,540,291,571,614,372,295,537,568,611,369,296,538,569,612,370,294,539,570,613,371,683,675,680,681,66,229,21,555,531,22,67,556,532,230,20,228,65,557,533,62,24,225,558,534,63,25,226,559,535,64,23,227,560,536,72,19,235,553,529,73,17,236,554,530,71,18,234,552,528,15,68,231,549,525,16,69,232,550,526,14,70,233,551,527,689,688,692,691 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#11540e60a31227d97822464caf7bd085f23c491501101f6992da34196185b51e, 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 15:18:47 · history