Equation 677 Database

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Magma f844a9e4ed51…

magma f844a9e4ed51
Size
705
Isomorphism class hash
f844a9e4ed516c3b8b9ef942a4147935665af49e1eb2bb261e2a621f7cd82984
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 17:28:08
Display reorder
660,245,571,105,447,168,246,572,103,448,166,104,247,446,167,570,574,244,101,450,171,575,242,102,451,169,573,243,100,449,170,251,577,111,453,163,252,578,109,454,164,253,576,110,452,165,456,580,250,107,162,581,248,108,457,160,579,249,106,455,161,672,671,669,666,22,333,351,291,349,20,334,352,292,347,350,21,290,348,332,336,25,354,294,345,337,23,355,295,346,335,24,353,293,344,17,331,357,297,340,18,329,358,298,338,19,330,356,296,339,300,327,16,360,343,328,14,361,301,341,326,15,359,299,342,688,685,687,686,46,459,363,485,535,44,460,364,486,536,362,45,484,534,458,462,49,366,488,538,463,47,367,489,539,461,48,365,487,537,41,465,369,491,541,42,466,370,492,542,43,464,368,490,540,494,468,40,372,544,469,38,373,495,545,467,39,371,493,543,663,667,670,668,266,399,497,583,375,267,400,498,584,376,496,268,582,374,398,402,269,500,586,378,403,270,501,587,379,401,271,499,585,377,272,405,503,589,381,273,406,504,590,382,274,404,502,588,380,592,408,275,506,384,409,276,507,593,385,407,277,505,591,383,679,676,674,682,174,411,315,283,313,172,412,316,281,311,314,173,282,312,410,414,177,318,279,309,415,175,319,280,310,413,176,317,278,308,180,417,321,289,304,178,418,322,287,302,179,416,320,288,303,285,420,183,324,307,421,181,325,286,305,419,182,323,284,306,661,665,662,664,257,152,547,523,93,258,153,548,524,91,546,259,522,92,151,148,256,550,526,89,149,254,551,527,90,150,255,549,525,88,263,158,553,529,99,264,159,554,530,97,265,157,552,528,98,532,154,262,556,95,155,260,557,533,96,156,261,555,531,94,696,693,697,695,61,509,87,1,471,59,623,622,621,620,86,60,0,470,508,631,57,629,630,628,635,58,633,634,632,627,56,624,626,625,52,643,640,642,641,50,647,644,646,645,51,639,636,638,637,654,655,55,652,653,659,53,656,658,657,651,54,648,650,649,701,704,702,703,219,193,217,595,204,220,194,215,596,205,216,218,594,206,192,189,222,213,598,203,190,223,214,599,201,191,221,212,597,202,225,187,208,601,195,226,188,209,602,196,224,186,207,600,197,604,184,228,211,198,619,229,618,605,199,185,227,210,603,200,699,700,694,698,134,607,473,511,8,135,608,474,512,9,472,133,510,10,606,610,130,476,514,11,611,131,477,515,12,609,132,475,513,13,125,613,479,517,6,126,614,480,518,7,124,612,478,516,5,520,616,128,482,2,617,129,483,521,3,615,127,481,519,4,678,684,683,680,237,559,387,435,81,238,560,388,436,82,386,236,434,80,558,562,240,390,438,84,563,241,391,439,85,561,239,389,437,83,235,565,393,441,79,233,566,394,442,77,234,564,392,440,78,444,568,231,396,75,569,232,397,445,76,567,230,395,443,74,675,681,673,677,29,423,68,142,116,30,424,69,143,117,70,31,144,115,422,426,28,71,145,112,427,26,72,146,113,425,27,73,147,114,35,429,66,140,122,36,430,67,141,123,37,428,65,139,121,136,432,34,62,118,433,32,63,137,119,431,33,64,138,120,690,689,691,692 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#5779f8cee5daac7ffda88b67b379fba3aadfa70634d24364b86a2ac7cf85bc20, 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 17:28:09 · history