Equation 677 Database

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Magma e785902c6119…

magma e785902c6119
Size
705
Isomorphism class hash
e785902c61193edd4db5fdddbf2a9ef026e37f10b19d767574d316c88ebc242a
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 19:44:16
Display reorder
660,577,505,219,397,0,578,506,217,398,2,579,507,218,399,1,504,576,215,396,4,502,574,216,394,5,575,503,214,395,3,210,496,568,388,7,208,497,569,389,8,209,498,570,390,6,499,213,571,391,10,500,211,572,392,11,501,212,573,393,9,670,666,668,663,529,20,110,164,247,530,18,111,165,248,531,19,112,166,249,23,528,113,167,246,21,526,114,168,244,527,22,115,169,245,108,15,520,162,253,109,16,521,163,254,107,17,522,161,255,14,104,523,158,252,12,105,524,159,250,13,106,525,160,251,689,690,686,685,635,553,287,517,589,636,554,288,518,590,637,555,286,519,591,552,634,290,516,588,550,632,291,514,586,633,551,289,515,587,285,544,626,508,580,283,545,627,509,581,284,546,628,510,582,547,281,629,511,583,548,282,630,512,584,549,280,631,513,585,672,669,671,667,338,373,86,565,173,339,374,87,566,174,337,375,88,567,175,372,334,89,564,172,370,335,90,562,170,336,371,91,563,171,84,364,329,556,179,85,365,330,557,180,83,366,328,558,181,367,80,332,559,178,368,81,333,560,176,369,82,331,561,177,682,674,678,680,469,361,97,445,340,470,362,95,446,341,471,363,96,447,342,360,468,93,444,343,358,466,94,442,344,467,359,92,443,345,103,352,460,436,346,101,353,461,437,347,102,354,462,438,348,355,99,463,439,349,356,100,464,440,350,357,98,465,441,351,665,661,662,664,412,305,270,316,433,413,306,268,317,434,414,304,269,318,435,308,415,273,319,432,309,416,271,320,430,417,307,272,321,431,276,311,418,322,424,274,312,419,323,425,275,310,420,324,426,314,279,421,325,427,315,277,422,326,428,313,278,423,327,429,694,693,696,698,613,48,37,647,61,655,654,38,652,653,657,656,36,658,659,51,612,40,644,60,49,610,41,645,58,611,50,39,646,59,43,55,604,639,67,44,56,605,640,65,42,57,606,638,66,54,46,607,642,63,52,47,608,643,64,53,45,609,641,62,701,703,704,702,541,192,225,385,188,542,648,223,386,649,543,651,224,387,650,195,540,221,384,189,193,538,222,382,190,539,194,220,383,191,231,144,532,376,186,229,145,533,377,187,230,143,534,378,185,140,227,535,379,182,141,228,536,380,183,142,226,537,381,184,697,699,700,695,601,493,74,202,24,602,494,75,203,25,603,495,76,204,26,492,600,77,205,27,490,598,78,206,28,599,491,79,207,29,72,484,592,200,30,73,485,593,201,31,71,486,594,199,32,487,68,595,196,33,488,69,596,197,34,489,70,597,198,35,683,676,677,673,157,409,132,235,623,155,410,133,236,624,156,411,131,237,625,408,153,128,234,622,406,154,129,232,620,152,407,130,233,621,138,400,148,241,614,139,401,146,242,615,137,402,147,243,616,403,134,151,240,617,404,135,149,238,618,405,136,150,239,619,679,675,684,681,292,121,265,457,481,293,119,266,458,482,294,120,267,459,483,117,295,264,456,480,118,296,262,454,478,297,116,263,455,479,256,127,298,448,472,257,125,299,449,473,258,126,300,450,474,123,259,301,451,475,124,260,302,452,476,122,261,303,453,477,688,691,692,687 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#a687d51fdba056b88b615f4c33c4bd51079879725771af3a621b4a64ac93acf2, 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 19:44:16 · history