Equation 677 Database

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Magma 0fd8550aa6d2…

magma 0fd8550aa6d2
Size
705
Isomorphism class hash
0fd8550aa6d2f2a1dca4dad6c7857676a2292a33343fd21cbaafe2d25c3dc6af
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 17:40:27
Display reorder
704,473,514,497,418,474,419,512,498,475,417,513,499,414,476,510,500,415,477,511,501,416,478,509,502,495,409,505,471,496,410,503,472,494,408,504,470,412,491,508,467,413,492,506,468,411,493,507,469,484,482,483,480,481,479,490,488,485,486,487,489,662,660,663,661,339,324,317,78,340,79,325,315,341,80,326,316,81,338,327,313,82,336,328,314,83,337,329,312,323,76,330,345,321,77,331,346,322,75,332,347,72,319,333,344,73,320,334,342,74,318,335,343,359,357,358,355,356,354,350,348,352,353,351,349,688,691,689,690,550,533,526,434,548,435,534,524,549,436,535,525,433,546,536,522,431,547,537,523,432,545,538,521,517,440,531,541,515,441,532,539,516,442,530,540,439,520,527,544,437,518,528,542,438,519,529,543,551,552,553,554,555,556,557,558,562,560,561,559,668,671,669,670,116,107,92,200,114,198,105,90,115,199,106,91,203,119,103,95,201,117,104,93,202,118,102,94,87,195,98,111,88,196,96,112,89,197,97,113,194,86,101,110,192,84,99,108,193,85,100,109,123,124,125,122,120,121,129,130,127,128,126,131,676,678,677,679,40,26,17,215,41,213,24,15,39,214,25,16,211,36,29,13,212,37,27,14,210,38,28,12,23,206,32,46,21,204,30,47,22,205,31,45,209,19,35,42,207,20,33,43,208,18,34,44,9,10,11,8,6,7,1,0,5,3,4,2,664,666,665,667,657,656,659,658,648,650,649,651,653,654,652,655,642,640,641,643,646,644,645,647,638,636,637,639,623,622,621,620,615,614,613,612,619,618,617,616,634,635,633,632,626,627,624,625,630,631,629,628,430,428,429,426,427,425,421,422,611,424,420,423,695,692,694,693,152,189,174,141,150,142,190,175,151,143,191,176,140,155,188,177,138,153,186,178,139,154,187,179,172,132,180,147,173,133,181,148,171,134,182,149,135,168,183,146,136,169,184,144,137,170,185,145,159,160,161,158,156,157,165,166,163,164,162,167,703,700,702,701,241,233,218,53,242,51,231,216,240,52,232,217,49,244,229,221,50,245,230,219,48,243,228,220,224,59,239,247,222,57,237,248,223,58,238,246,55,227,235,250,56,225,236,251,54,226,234,249,260,258,259,263,261,262,255,256,253,254,252,257,699,696,698,697,362,399,385,466,360,464,400,386,361,465,401,384,462,365,398,388,463,363,396,389,461,364,397,387,391,457,405,368,392,455,406,366,390,456,407,367,460,394,404,371,458,395,402,369,459,393,403,370,379,380,378,382,383,381,377,375,372,373,374,376,672,675,673,674,286,272,309,68,287,66,270,310,285,67,271,311,71,282,275,308,69,283,273,306,70,284,274,307,300,63,267,277,301,64,268,278,302,65,269,276,62,303,266,280,60,304,264,281,61,305,265,279,290,288,289,293,291,292,296,294,298,299,297,295,681,680,682,683,608,594,584,452,609,453,595,585,610,454,593,586,451,607,597,583,449,605,598,581,450,606,596,582,575,443,592,599,576,444,590,600,577,445,591,601,446,578,588,602,447,579,589,603,448,580,587,604,564,565,563,567,568,566,570,571,572,573,574,569,686,684,687,685 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#5e80e1c2dc82944cee69cb7089d21c45f5ab65bc382c5d130a060fbb3f31d2ae, 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 17:40:29 · history