Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma a994462bf4a6…

magma a994462bf4a6
Size
705
Isomorphism class hash
a994462bf4a6595f0e8012fcb895ebf52336487c4839d39e84cfd1f2d665be01
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 16:29:31
Display reorder
660,530,203,525,532,529,490,201,489,485,492,510,202,509,505,512,452,199,451,450,454,470,200,469,465,472,430,198,429,425,432,650,194,649,645,652,192,609,605,610,612,193,629,625,630,632,569,197,565,570,572,589,195,585,590,592,549,196,545,550,552,687,685,701,699,533,29,528,526,527,493,27,487,488,486,513,28,507,508,506,455,25,443,444,442,473,26,467,468,466,433,24,427,428,426,653,35,647,648,646,33,607,608,613,606,34,627,628,633,626,567,31,568,573,566,587,32,588,593,586,547,30,548,553,546,697,694,703,690,305,224,259,353,341,303,222,339,260,351,304,223,340,258,352,301,227,337,262,349,302,225,338,263,350,300,226,336,261,348,311,219,347,257,359,220,345,255,309,357,221,346,256,310,358,343,218,253,307,355,344,216,254,308,356,342,217,252,306,354,665,663,668,682,103,46,389,80,87,104,47,88,387,78,102,45,89,388,79,106,42,86,385,83,107,43,84,386,81,105,44,85,384,82,101,37,93,395,75,38,94,393,99,76,36,95,394,100,77,92,40,391,97,74,90,41,392,98,72,91,39,390,96,73,677,667,675,680,535,127,521,531,523,495,128,483,481,491,515,126,503,501,511,457,130,447,448,453,478,131,462,463,471,437,129,423,421,431,655,125,642,643,651,123,602,603,615,611,124,622,623,635,631,562,121,563,575,571,582,122,583,595,591,542,120,543,555,551,700,695,689,692,524,61,537,539,536,484,62,496,497,499,504,60,516,517,519,449,64,458,456,459,464,65,476,477,479,424,63,438,436,439,644,67,656,657,659,68,616,617,604,619,66,636,637,624,639,576,70,577,564,579,596,71,597,584,599,556,69,557,544,559,688,686,691,696,538,4,534,520,522,498,5,482,494,480,518,3,502,514,500,446,1,441,445,440,475,0,460,474,461,435,2,422,434,420,658,10,641,654,640,11,601,614,618,600,9,621,634,638,620,560,6,574,578,561,580,7,594,598,581,540,8,554,558,541,704,698,702,693,142,117,401,154,167,143,118,165,399,155,141,119,166,400,153,138,116,163,397,150,139,114,164,398,151,140,115,162,396,152,133,108,158,407,145,109,156,405,134,146,110,157,406,132,144,161,111,403,136,148,159,112,404,137,149,160,113,402,135,147,670,679,672,683,228,14,413,244,59,229,12,57,411,245,230,13,58,412,243,231,17,55,409,240,232,15,56,410,241,233,16,54,408,242,234,20,50,419,250,18,48,417,235,251,19,49,418,236,249,53,23,415,237,246,51,21,416,238,247,52,22,414,239,248,673,681,676,684,284,213,180,293,265,282,214,266,181,291,283,215,264,182,292,287,212,268,183,289,285,210,269,184,290,286,211,267,185,288,279,204,271,186,299,205,272,187,280,297,206,270,188,281,298,274,207,189,278,295,275,208,190,276,296,273,209,191,277,294,678,669,661,666,320,175,377,329,365,318,176,363,375,327,319,174,364,376,328,323,178,361,373,325,321,179,362,374,326,322,177,360,372,324,315,173,371,383,335,171,369,381,316,333,172,370,382,317,334,367,169,379,314,331,368,170,380,312,332,366,168,378,313,330,671,662,664,674 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#33fc7ab4b4817466950310b35dd4cd44cb4b00aed5b55945bbae0672c2180aa2, 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 16:29:32 · history