Equation 677 Database

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Magma 1d2388954ba6…

magma 1d2388954ba6
Size
705
Isomorphism class hash
1d2388954ba62681c744f6fe4133cb0b0f1465e7349a23c8541fce2d7d504705
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 20:43:06
Display reorder
704,490,13,508,474,491,14,475,509,489,12,476,507,16,486,504,477,17,487,505,478,488,15,479,506,19,481,514,472,482,20,473,515,480,18,471,513,22,484,510,468,485,23,469,511,483,21,470,512,499,500,498,502,503,501,497,495,492,493,494,496,662,660,663,661,155,287,122,138,153,285,139,120,154,286,140,121,283,151,125,141,284,152,123,142,150,282,143,124,278,146,128,136,144,276,137,126,145,277,135,127,281,149,131,132,147,279,133,129,148,280,134,130,119,117,118,115,116,114,110,108,112,113,111,109,688,691,689,690,563,397,530,546,561,398,547,528,562,396,548,529,400,559,533,549,401,560,531,550,558,399,551,532,403,554,536,544,552,404,545,534,553,402,543,535,406,557,539,540,555,407,541,537,556,405,542,538,527,525,526,523,524,522,518,516,520,521,519,517,668,671,669,670,295,164,314,332,296,162,330,312,294,163,331,313,167,298,317,335,165,299,315,333,297,166,334,316,159,293,320,327,291,160,328,318,292,161,329,319,158,289,323,326,290,156,324,321,288,157,325,322,309,310,311,308,306,307,300,301,305,303,304,302,676,678,677,679,355,179,373,346,356,177,347,374,354,178,345,372,175,358,376,342,176,359,377,343,357,174,344,375,170,353,379,337,351,168,338,380,352,169,336,378,173,349,382,340,350,171,341,383,348,172,339,381,371,369,370,367,368,366,362,360,364,365,363,361,664,666,665,667,656,658,657,659,648,650,651,649,652,654,655,653,642,640,641,643,646,645,644,647,636,638,639,637,622,620,621,623,613,612,614,615,616,618,619,617,632,634,633,635,626,625,627,624,630,629,631,628,392,390,391,395,393,394,387,388,385,386,384,389,695,692,694,693,55,26,72,45,56,24,46,73,54,25,47,74,29,58,75,44,27,59,76,42,57,28,43,77,32,53,78,36,51,30,37,79,52,31,38,80,35,49,81,39,50,33,40,82,48,34,41,83,71,69,70,67,68,66,62,60,64,65,63,61,703,700,702,701,196,90,224,182,197,91,180,222,195,92,181,223,93,192,227,185,94,193,225,183,194,95,184,226,88,202,219,188,203,89,186,220,201,87,187,221,84,198,218,191,199,85,189,216,200,86,190,217,205,206,204,208,209,207,211,212,213,214,215,210,699,696,698,697,430,2,447,467,431,1,465,448,429,0,466,449,5,426,446,463,3,427,444,464,428,4,462,445,8,421,453,458,422,6,456,454,420,7,457,455,11,424,452,461,425,9,459,450,423,10,460,451,439,440,438,442,443,441,437,435,432,433,434,436,672,675,673,674,247,107,265,238,248,105,239,266,246,106,237,264,103,250,268,234,104,251,269,235,249,102,236,267,98,245,271,229,243,96,230,272,244,97,228,270,101,241,274,232,242,99,233,275,240,100,231,273,261,262,263,260,258,259,252,253,257,255,256,254,681,680,682,683,609,410,576,595,610,408,596,577,611,409,594,578,413,608,579,598,411,606,580,599,607,412,597,581,416,600,582,593,601,414,591,583,602,415,592,584,419,603,585,589,604,417,590,586,605,418,588,587,574,575,573,570,571,572,565,566,567,568,569,564,686,684,687,685 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#cce41c1fd55a940f76617a374756c8d0de5f99032cd8fe3feeb0eb2c48843df6, 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 20:43:07 · history