Equation 677 Database

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Magma c9c204eb50dc…

magma c9c204eb50dc
Size
705
Isomorphism class hash
c9c204eb50dc943335f34f39f6f474ae968b6ad819505882d78fce8c05f55496
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 15:57:23
Display reorder
660,382,346,270,406,322,383,347,407,268,323,384,348,269,408,324,345,381,266,405,321,343,379,267,403,319,344,380,265,404,320,352,412,388,261,328,353,413,389,259,329,354,414,390,260,330,411,351,387,264,327,409,349,385,262,325,410,350,386,263,326,662,672,663,664,394,334,127,249,184,395,335,247,128,185,396,336,129,248,186,333,393,130,252,183,331,391,131,250,181,332,392,132,251,182,340,255,400,133,175,341,253,401,134,176,342,254,402,135,177,258,339,399,136,178,256,337,397,137,179,257,338,398,138,180,686,691,687,685,52,80,292,513,365,53,78,514,293,366,51,79,294,515,364,76,55,291,512,361,77,56,289,510,362,75,54,290,511,363,71,519,50,283,356,69,520,48,284,357,70,521,49,285,355,518,74,46,286,359,516,72,47,287,360,517,73,45,288,358,670,661,669,667,200,583,14,188,501,201,584,189,12,502,199,585,13,187,503,582,203,17,191,500,580,204,15,192,498,581,202,16,190,499,589,194,206,20,507,590,195,207,18,508,591,193,205,19,509,197,588,209,23,506,198,586,210,21,504,196,587,208,22,505,680,677,682,673,140,535,218,631,465,141,536,632,219,466,139,537,217,633,467,534,143,221,630,464,532,144,222,628,462,533,142,220,629,463,541,637,146,216,471,542,638,147,214,472,543,639,145,215,473,636,540,149,212,470,634,538,150,213,468,635,539,148,211,469,668,665,666,671,272,370,61,430,571,273,371,431,62,572,271,372,60,432,573,369,275,57,429,570,367,276,58,427,568,368,274,59,428,569,376,436,278,67,577,377,437,279,68,578,378,438,277,66,579,435,375,281,63,576,433,373,282,64,574,434,374,280,65,575,694,698,693,695,525,451,112,123,40,526,452,121,113,41,527,453,111,122,39,454,524,115,119,36,455,522,116,120,37,456,523,114,118,38,457,117,531,110,461,655,653,654,108,652,656,658,659,109,657,125,458,530,106,42,126,459,528,107,43,124,460,529,105,44,702,701,704,703,233,607,154,559,442,234,608,560,155,443,232,609,156,561,444,606,229,153,558,441,604,230,151,556,439,605,231,152,557,440,613,565,224,160,448,614,566,225,161,449,615,567,223,162,450,564,612,227,159,447,562,610,228,157,445,563,611,226,158,446,700,696,699,697,547,477,313,2,595,548,478,1,314,596,549,479,315,0,597,476,546,316,5,594,474,544,317,3,592,475,545,318,4,593,483,8,553,311,601,484,6,554,312,602,485,7,555,310,603,11,482,552,307,600,9,480,550,308,598,10,481,551,309,599,675,681,679,684,418,171,235,489,643,419,169,490,236,644,420,170,237,491,645,174,417,238,488,642,172,415,239,486,640,173,416,240,487,641,166,495,424,241,649,167,496,425,242,650,168,497,426,243,651,494,165,423,244,648,492,163,421,245,646,493,164,422,246,647,678,683,674,676,619,88,304,96,29,620,89,97,305,27,621,87,306,98,28,91,618,303,95,25,92,616,301,93,26,90,617,302,94,24,86,102,625,295,35,84,103,626,296,33,85,104,627,297,34,101,82,624,298,31,99,83,622,299,32,100,81,623,300,30,689,690,692,688 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#25532901b7174194dca0f8f453aa2ae473cc5b2aa34d04b35f0c3beb206af29c, 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 15:57:24 · history