Equation 677 Database

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Magma 3bc3ffa6d166…

magma 3bc3ffa6d166
Size
705
Isomorphism class hash
3bc3ffa6d166d00a44c72361f3d38411827f3575684698d154a0dfca6d8ee808
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 15:09:47
Display reorder
660,340,150,350,223,231,341,148,351,224,229,342,149,349,225,230,343,153,346,222,227,151,344,347,220,228,345,152,348,221,226,338,145,356,214,237,339,146,357,215,235,337,147,355,216,236,144,334,352,217,233,142,335,353,218,234,143,336,354,219,232,669,672,668,661,624,108,283,589,541,625,106,284,590,542,623,107,285,588,540,620,111,282,585,537,109,621,280,586,538,622,110,281,587,539,630,114,274,595,547,631,112,275,596,548,629,113,276,594,546,117,626,277,591,543,115,627,278,592,544,116,628,279,593,545,690,686,691,685,434,183,470,43,601,435,181,471,44,602,433,182,469,42,600,430,179,466,46,597,180,431,467,47,598,432,178,468,45,599,440,189,476,41,607,441,187,477,39,608,439,188,475,40,606,185,436,472,37,603,186,437,473,38,604,184,438,474,36,605,665,670,663,664,458,293,482,422,70,459,294,483,423,71,457,292,481,421,69,454,296,478,418,66,297,455,479,419,67,456,295,480,420,68,464,291,488,428,61,465,289,489,429,62,463,290,487,427,60,287,460,484,424,64,288,461,485,425,65,286,462,486,426,63,675,682,677,679,10,366,636,553,241,11,364,637,554,242,9,365,635,552,243,6,369,632,549,240,367,7,633,550,238,8,368,634,551,239,0,361,642,559,247,2,362,643,560,248,1,363,641,558,249,360,4,638,555,246,358,5,639,556,244,359,3,640,557,245,667,662,666,671,494,29,163,171,577,495,27,164,169,578,493,28,165,170,576,490,25,162,167,573,26,491,160,168,574,492,24,161,166,575,500,35,154,177,583,501,33,155,175,584,499,34,156,176,582,31,496,157,173,579,32,497,158,174,580,30,498,159,172,581,693,699,695,694,93,54,530,613,96,94,55,531,614,97,92,56,529,612,95,89,57,526,609,99,58,90,527,610,100,91,59,528,611,98,84,52,536,619,102,659,53,656,658,657,85,51,535,618,101,48,87,532,615,105,49,88,533,616,103,50,86,534,617,104,704,703,702,701,518,256,380,382,395,519,257,381,383,396,517,258,379,384,394,514,259,376,385,398,260,515,377,386,399,516,261,378,387,397,524,254,371,388,401,525,255,372,389,402,523,253,370,390,400,250,520,374,391,404,251,521,375,392,405,252,522,373,393,403,700,697,696,698,446,13,213,506,332,447,14,211,507,333,445,12,212,505,331,442,16,209,502,328,17,443,210,503,329,444,15,208,504,330,452,19,204,512,323,453,20,202,513,324,451,18,203,511,322,22,448,207,508,326,23,449,205,509,327,21,450,206,510,325,680,678,676,684,302,270,565,410,648,303,268,566,411,649,301,269,564,409,647,298,273,561,406,644,271,299,562,407,645,300,272,563,408,646,308,265,571,416,654,309,266,572,417,655,307,267,570,415,653,264,304,567,412,650,262,305,568,413,651,263,306,569,414,652,674,683,673,681,134,194,318,75,124,135,195,316,76,125,133,193,317,77,126,130,190,321,74,127,191,131,319,72,128,132,192,320,73,129,140,200,313,81,122,141,201,314,82,123,139,199,315,83,121,196,136,312,80,118,197,137,310,78,119,198,138,311,79,120,689,688,687,692 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#05c0aaa7a3560fa146ae1951a40d178d675f2688aa4f7579703e2b967da3180b, 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 15:09:47 · history