Equation 677 Database

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Magma 2ebe4510a0a1…

magma 2ebe4510a0a1
Size
705
Isomorphism class hash
2ebe4510a0a1fcea788656f936c9930ec7abebde2e82a5d5532a6dcac5c70ef4
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 18:13:26
Display reorder
660,407,335,92,173,0,405,333,171,90,2,406,334,172,91,1,403,331,169,88,4,332,404,170,89,5,330,402,168,87,3,413,341,83,164,7,411,339,81,162,8,412,340,82,163,6,409,337,86,167,10,410,338,84,165,11,408,336,85,166,9,663,672,661,662,22,375,455,292,383,23,376,293,453,381,21,377,291,454,382,18,374,288,451,379,372,19,289,452,380,373,20,290,450,378,13,366,461,283,389,14,367,459,284,387,12,368,460,282,388,16,369,457,286,385,17,370,458,287,386,15,371,456,285,384,686,687,691,688,593,109,479,191,443,591,110,189,477,441,592,108,190,478,442,589,105,187,475,439,106,590,188,476,440,107,588,186,474,438,599,115,485,197,449,597,116,483,195,447,598,114,484,196,448,595,111,481,193,445,596,112,482,194,446,594,113,480,192,444,670,664,669,665,33,431,581,304,524,34,429,305,579,522,35,430,303,580,523,32,427,300,577,520,428,30,301,578,521,426,31,302,576,519,24,437,587,295,530,25,435,585,296,528,26,436,586,294,529,27,433,583,298,526,28,434,584,299,527,29,432,582,297,525,675,678,682,680,545,562,629,308,563,543,559,306,627,558,544,561,307,628,560,541,554,311,625,555,556,542,309,626,557,552,540,310,624,553,551,574,635,314,575,549,571,633,312,570,550,572,634,313,573,547,566,631,317,567,548,568,632,315,569,546,565,630,316,564,667,668,666,671,359,605,395,95,351,357,603,93,393,352,358,604,94,394,353,355,601,98,391,350,602,356,96,392,348,600,354,97,390,349,365,611,401,101,342,363,609,399,99,343,364,610,400,100,344,361,607,397,104,345,362,608,398,102,346,360,606,396,103,347,699,693,695,696,490,124,79,181,536,491,125,182,80,534,489,123,180,78,535,486,120,184,75,532,121,487,185,76,533,122,488,183,77,531,656,657,658,179,659,651,648,649,177,650,652,653,654,178,655,492,118,73,175,538,493,119,74,176,539,494,117,72,174,537,701,704,702,703,258,323,467,44,246,259,321,42,465,247,260,322,43,466,248,261,319,47,463,249,320,262,45,464,250,318,263,46,462,251,264,329,473,39,252,265,327,471,40,253,266,328,472,41,254,267,325,469,38,255,268,326,470,36,256,269,324,468,37,257,694,700,698,697,222,160,234,61,500,223,161,62,235,498,224,159,60,236,499,225,156,64,237,496,157,226,65,238,497,158,227,63,239,495,228,151,240,67,506,229,152,241,68,504,230,150,242,66,505,231,154,243,70,502,232,155,244,71,503,233,153,245,69,501,673,677,676,684,419,140,127,275,641,417,138,273,128,639,418,139,274,126,640,415,143,271,130,637,141,416,272,131,638,142,414,270,129,636,425,146,133,281,647,423,144,134,279,645,424,145,132,280,646,421,149,136,277,643,422,147,137,278,644,420,148,135,276,642,681,683,674,679,617,201,512,52,220,615,202,53,510,221,616,203,51,511,219,613,200,48,508,216,198,614,49,509,217,199,612,50,507,218,623,207,518,58,211,621,208,516,59,212,622,209,517,57,210,619,206,514,54,214,620,204,515,55,215,618,205,513,56,213,689,685,692,690 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#6b720d896a29843112ad3c0147d655cf7bb7a1ca51519c2978dbef59d093ebaf, 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 18:13:27 · history