Equation 677 Database

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Magma 7b8fa1613c63…

magma 7b8fa1613c63
Size
705
Isomorphism class hash
7b8fa1613c630913e518c5934880f8af5d21b89ff5f175f0272cadbdd93103ef
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 19:49:53
Display reorder
704,498,2,463,469,1,499,464,470,0,500,462,468,501,5,466,472,502,3,467,473,503,4,465,471,8,461,496,475,6,459,497,476,7,460,495,474,457,11,492,478,458,9,493,479,456,10,494,477,489,490,491,488,486,487,480,481,485,483,484,482,662,661,663,660,192,121,204,217,122,193,205,218,120,194,206,216,195,124,207,220,196,125,208,221,197,123,209,219,127,210,198,223,128,211,199,224,126,212,200,222,213,130,201,226,214,131,202,227,215,129,203,225,181,182,180,184,185,183,187,188,189,190,191,186,688,690,689,691,560,423,522,532,424,558,523,533,425,559,524,531,563,422,525,528,561,420,526,529,562,421,527,530,429,520,555,538,430,521,556,539,431,519,557,537,516,428,554,534,517,426,552,535,518,427,553,536,543,544,545,542,540,541,549,550,547,548,546,551,668,670,669,671,258,137,269,231,135,259,267,232,136,260,268,233,261,133,265,230,262,134,266,228,263,132,264,229,143,275,256,237,141,273,257,238,142,274,255,239,271,139,252,236,272,140,253,234,270,138,254,235,249,250,251,248,246,247,240,241,245,243,244,242,676,679,677,678,277,149,298,307,147,278,299,308,148,276,297,306,280,145,294,310,281,146,295,311,279,144,296,309,155,289,283,305,153,290,284,303,154,288,282,304,292,151,286,301,293,152,287,302,291,150,285,300,314,312,313,317,315,316,320,318,322,323,321,319,664,667,665,666,657,659,656,658,651,648,649,650,655,653,652,654,640,643,641,642,644,647,645,646,637,639,636,638,623,621,620,622,615,613,612,614,619,617,616,618,633,635,632,634,624,627,625,626,628,631,629,630,509,507,508,505,506,504,515,513,510,511,512,514,695,693,694,692,28,16,41,54,17,29,39,55,15,27,40,56,24,12,37,57,25,13,38,58,26,14,36,59,22,47,34,52,23,45,35,53,21,46,33,51,43,18,30,48,44,19,31,49,42,20,32,50,64,65,63,60,61,62,70,71,68,66,67,69,703,701,702,700,348,160,360,333,161,349,361,334,159,350,362,335,351,156,363,332,352,157,364,330,353,158,365,331,166,366,354,324,167,367,355,325,165,368,356,326,369,162,357,327,370,163,358,328,371,164,359,329,337,338,336,340,341,339,343,344,345,346,347,342,699,697,698,696,115,454,78,88,455,116,79,89,453,114,80,87,118,450,81,84,119,451,82,85,117,452,83,86,445,76,113,94,446,77,111,95,444,75,112,93,72,448,109,90,73,449,110,91,74,447,108,92,99,100,101,98,96,97,105,106,103,104,102,107,672,674,673,675,373,171,394,403,172,374,395,404,173,372,393,402,376,170,390,406,377,168,391,407,375,169,392,405,177,385,379,401,178,386,380,399,179,384,378,400,388,176,382,397,389,174,383,398,387,175,381,396,410,408,409,413,411,412,416,414,418,419,417,415,681,683,682,680,591,441,609,571,442,592,610,572,443,593,611,570,590,440,608,574,588,438,606,575,589,439,607,573,432,600,597,569,433,601,598,567,434,602,599,568,603,435,596,565,604,436,594,566,605,437,595,564,576,577,578,579,580,581,582,583,587,585,586,584,686,685,687,684 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#adb39c7b26968070fd85ec3ca227f43c35cfd242a3390aaf8597bfe24e1ed89b, 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 19:49:54 · history