Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma ccb2d90b898c…

magma ccb2d90b898c
Size
705
Isomorphism class hash
ccb2d90b898c6dc929ba92e7157e120c5714f1ce0acc8d2bdd2ae1b73bcc1926
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 16:43:11
Display reorder
660,18,444,527,183,175,19,184,445,528,176,446,185,20,529,174,186,21,443,526,171,187,22,441,524,172,188,23,442,525,173,435,189,518,16,181,436,190,519,17,182,437,191,520,15,180,192,438,521,12,177,193,439,522,13,178,194,440,523,14,179,665,661,671,666,28,456,539,269,265,29,267,457,540,266,458,268,27,541,264,272,24,455,538,261,270,25,453,536,262,271,26,454,537,263,447,275,530,34,256,448,273,531,35,257,449,274,532,33,255,278,450,533,30,259,276,451,534,31,260,277,452,535,32,258,686,690,685,687,41,376,340,635,396,39,636,377,341,397,375,637,40,339,398,634,37,379,343,395,632,38,380,344,393,633,36,378,342,394,382,626,346,47,387,383,627,347,45,388,381,628,345,46,389,629,385,349,43,390,630,386,350,44,391,631,384,348,42,392,662,663,672,669,285,432,360,117,214,286,115,433,361,215,434,116,287,362,213,120,288,431,359,217,118,289,429,357,218,119,290,430,358,216,423,123,351,283,212,424,121,352,284,210,425,122,353,282,211,126,426,354,279,208,124,427,355,280,209,125,428,356,281,207,677,681,684,674,301,575,420,599,551,302,600,576,421,552,577,601,300,422,553,598,297,574,419,550,596,298,572,417,548,597,299,573,418,549,566,590,411,292,542,567,591,412,293,543,568,592,413,291,544,593,569,414,295,545,594,570,415,296,546,595,571,416,294,547,668,667,670,664,97,462,408,61,480,98,62,463,409,481,464,60,99,410,482,64,100,461,407,479,65,101,459,405,477,63,102,460,406,478,468,67,399,95,471,469,68,400,96,472,470,66,401,94,473,70,467,402,91,474,71,465,403,92,475,69,466,404,93,476,694,697,693,696,329,501,505,647,161,327,655,654,652,653,656,659,328,657,658,646,332,502,80,162,644,330,503,78,163,645,331,504,79,164,499,638,72,335,165,500,639,73,333,166,498,640,74,334,167,641,495,75,338,168,642,496,76,336,169,643,497,77,337,170,703,701,704,702,135,157,305,515,81,133,516,648,303,649,650,517,134,304,651,514,138,158,308,83,512,136,159,306,84,513,137,160,307,82,155,506,311,130,86,156,507,309,131,87,154,508,310,132,85,509,151,314,129,89,510,152,312,127,90,511,153,313,128,88,700,699,698,695,206,623,3,372,240,204,373,624,4,241,625,374,205,5,242,371,202,622,2,239,369,203,620,1,237,370,201,621,0,238,614,363,9,197,231,615,364,10,195,232,616,365,11,196,233,366,617,8,200,234,367,618,6,198,235,368,619,7,199,236,683,680,675,682,114,319,492,251,140,112,249,320,493,141,318,250,113,494,139,254,110,315,491,143,252,111,316,489,144,253,109,317,490,142,325,246,483,105,146,326,247,484,103,147,324,248,485,104,145,245,321,486,108,149,243,322,487,106,150,244,323,488,107,148,676,678,673,679,223,563,611,53,587,224,51,564,612,588,565,52,222,613,589,49,219,562,610,586,50,220,560,608,584,48,221,561,609,585,554,59,602,229,578,555,57,603,230,579,556,58,604,228,580,55,557,605,225,581,56,558,606,226,582,54,559,607,227,583,688,689,691,692 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#3a4a415766bc24344b8990a318a493c1fb50830922fededbbeb9b2ef7d49358b, 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 16:43:12 · history