Equation 677 Database

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Magma f18cac1f7129…

magma f18cac1f7129
Size
705
Isomorphism class hash
f18cac1f7129560e94e2ea5d820c61d8d5dba0d413b801065c49ad858411bd12
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 20:35:58
Display reorder
660,275,48,453,525,203,276,204,46,451,523,47,202,274,452,524,278,44,206,449,521,45,279,207,450,522,277,43,205,448,520,281,39,209,444,516,282,37,210,442,514,443,280,38,208,515,42,284,212,447,519,40,285,213,445,517,41,283,211,446,518,669,665,667,672,73,375,98,465,365,74,366,373,99,463,374,364,75,97,464,72,371,368,94,461,372,70,369,95,462,71,370,367,96,460,79,381,363,104,456,80,379,361,105,454,103,81,380,362,455,377,78,359,100,459,378,76,360,101,457,376,77,358,102,458,686,687,689,690,236,501,247,572,18,237,16,499,248,570,500,17,235,249,571,232,497,14,246,568,498,233,15,244,569,234,496,13,245,567,227,492,24,238,563,228,490,22,239,561,240,226,491,23,562,495,230,20,241,566,493,231,21,242,564,494,229,19,243,565,670,666,662,668,403,559,158,560,86,404,87,556,159,555,558,85,405,157,557,402,552,82,154,551,553,400,83,155,554,401,550,84,156,549,394,542,92,164,541,395,538,93,165,1,163,396,539,91,540,547,397,88,160,548,543,398,89,161,544,545,399,90,162,546,680,673,675,679,390,441,593,411,419,388,420,439,591,409,440,418,389,592,410,393,437,422,589,407,438,391,423,590,408,392,436,421,588,406,385,432,425,584,417,386,430,426,582,415,583,387,431,424,416,435,384,428,587,413,433,382,429,585,414,434,383,427,586,412,661,671,663,664,221,291,299,319,477,222,475,289,300,320,290,476,220,298,321,224,287,473,302,318,288,225,474,303,316,223,286,472,301,317,219,297,468,305,310,217,295,466,306,311,304,218,296,467,312,293,215,471,308,313,294,216,469,309,314,292,214,470,307,315,696,697,694,695,56,657,658,659,656,57,650,651,648,649,653,652,55,654,655,59,63,579,619,618,61,60,580,621,620,58,62,581,622,623,54,66,574,609,608,52,64,575,610,611,607,53,65,573,606,69,50,577,615,614,67,51,578,617,616,68,49,576,613,612,703,704,701,702,327,201,646,647,180,325,178,199,643,642,200,179,326,644,645,323,197,183,638,639,198,324,181,640,641,322,196,182,637,636,333,192,186,628,629,331,190,184,625,624,626,332,191,185,627,195,329,189,634,635,193,330,187,631,630,194,328,188,633,632,700,699,698,693,270,132,152,489,123,268,121,130,153,487,131,122,269,151,488,273,135,119,148,485,133,271,120,149,486,272,134,118,150,484,265,138,129,143,480,266,136,127,144,478,142,267,137,128,479,141,264,125,146,483,139,262,126,147,481,140,263,124,145,482,674,683,684,678,10,605,513,604,335,11,336,600,511,601,602,334,12,512,603,9,596,338,509,597,599,7,339,510,598,8,595,337,508,594,0,347,341,504,355,2,348,342,502,356,503,3,346,340,357,350,4,344,507,354,351,5,345,505,352,349,6,343,506,353,681,676,677,682,115,28,537,259,168,116,166,29,535,260,30,167,117,536,261,114,27,171,533,258,25,112,169,534,256,113,26,170,532,257,106,34,174,528,250,107,35,172,526,251,527,108,36,173,252,33,109,177,531,253,31,110,175,529,254,32,111,176,530,255,685,688,692,691 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#c683f2f4b9bca41895c10e0d2ae80f929e5396dd75ded79bce8025bcd75f3dbe, 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 20:35:59 · history