Equation 677 Database

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Magma 31c2d4cf8e6b…

magma 31c2d4cf8e6b
Size
705
Isomorphism class hash
31c2d4cf8e6b2f88498df7b713b5d19d1a87dfa312c7e8fd9d5bbbd7200aef7a
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 20:36:26
Display reorder
660,444,451,184,443,455,464,471,463,185,475,421,425,183,428,435,514,506,180,505,519,534,526,181,525,539,494,486,182,485,499,574,566,190,565,579,594,586,191,585,599,554,546,189,545,559,626,634,186,625,639,646,654,187,645,659,606,614,188,605,619,685,694,703,691,441,450,55,447,440,461,470,467,56,462,420,424,54,430,426,513,502,58,509,500,533,522,59,529,520,493,482,57,489,481,573,562,53,569,561,593,582,51,589,581,553,542,52,549,541,622,633,49,629,620,642,653,50,649,640,602,613,48,609,601,701,697,688,692,1,385,269,399,301,0,386,401,267,302,2,384,268,396,300,388,3,265,405,304,389,4,266,407,305,387,5,264,403,303,391,6,275,410,307,392,7,273,412,308,390,8,274,408,306,9,394,271,416,310,10,395,272,418,311,11,393,270,414,309,662,681,666,678,133,373,115,314,398,134,374,312,116,400,132,372,114,313,397,376,136,118,317,404,377,137,119,315,406,375,135,117,316,402,379,139,113,320,411,380,140,111,318,413,378,138,112,319,409,142,382,109,323,417,143,383,110,321,419,141,381,108,322,415,668,674,680,676,446,452,259,458,459,466,472,476,260,477,429,432,258,436,437,515,508,262,510,501,535,528,263,530,521,495,488,261,490,480,575,568,257,570,560,595,588,255,590,580,555,548,256,550,540,628,635,253,630,621,648,655,254,650,641,608,615,252,610,600,695,699,702,690,457,456,155,453,448,479,478,473,153,468,439,438,154,433,431,518,504,151,516,511,538,524,152,536,531,498,484,150,496,491,578,564,146,576,571,598,584,144,596,591,558,544,145,556,551,624,638,149,636,631,644,658,147,656,651,604,618,148,616,611,686,696,698,689,442,454,67,449,445,460,474,469,68,465,427,434,66,423,422,517,503,70,512,507,537,523,71,532,527,497,483,69,492,487,577,563,65,572,567,597,583,63,592,587,557,543,64,552,547,623,637,61,632,627,643,657,62,652,647,603,617,60,612,607,693,704,687,700,249,337,100,129,289,250,338,130,101,290,251,336,99,131,288,340,248,96,128,292,341,246,97,126,293,339,247,98,127,291,343,240,106,120,295,344,241,107,121,296,342,242,105,122,294,243,346,102,123,298,244,347,103,124,299,245,345,104,125,297,670,682,664,671,277,159,33,177,325,278,160,178,34,326,276,161,35,179,324,158,280,32,176,328,156,281,30,174,329,157,279,31,175,327,165,283,24,168,331,166,284,25,169,332,167,282,26,170,330,286,164,27,171,334,287,162,28,172,335,285,163,29,173,333,663,667,669,675,229,194,44,207,225,230,192,208,42,226,228,193,43,209,227,197,232,47,206,224,195,233,45,204,222,196,231,46,205,223,200,235,39,213,216,198,236,40,214,217,199,234,41,215,218,238,203,38,212,219,239,201,36,210,220,237,202,37,211,221,661,665,677,683,349,72,12,95,361,350,73,93,13,362,348,74,14,94,360,75,352,18,91,364,76,353,21,92,365,77,351,23,90,363,78,355,20,86,367,79,356,22,84,368,80,354,19,85,366,358,81,17,89,370,359,82,15,87,371,357,83,16,88,369,672,679,673,684 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#c6a869941d5f836cd5f826f4a41a523fb37d651c2417bcc51f4579b275cefef3, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 20:36:27 · history