Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 22e39c16ab13…

magma 22e39c16ab13
Size
705
Isomorphism class hash
22e39c16ab13972f5e4b2d16acd3b3ef30b5a1513fd08d53ea8f06007c9da1a0
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 16:30:52
Display reorder
660,295,159,399,172,537,293,538,160,400,173,161,536,294,398,171,540,291,158,402,168,541,292,156,403,169,539,290,157,401,170,286,165,543,405,178,284,166,544,406,179,285,167,542,404,177,164,289,546,408,174,162,287,547,409,175,163,288,545,407,176,675,674,677,682,259,119,359,36,365,257,366,117,360,37,118,364,258,358,38,368,255,115,362,39,369,256,116,363,40,367,254,114,361,41,250,110,371,357,42,248,108,372,355,43,249,109,370,356,44,113,253,374,353,45,111,251,375,354,46,112,252,373,352,47,670,665,672,662,306,130,137,513,561,307,562,131,135,514,129,560,305,136,512,564,302,126,133,516,565,303,127,134,517,563,304,128,132,515,297,121,567,143,519,298,122,568,141,520,296,120,566,142,518,124,300,570,139,522,125,301,571,140,523,123,299,569,138,521,679,680,685,683,55,334,447,393,467,56,468,332,448,391,333,466,54,446,392,470,58,337,450,389,471,59,335,451,390,469,57,336,449,388,53,340,473,453,397,51,338,474,454,395,52,339,472,452,396,644,49,647,649,648,654,50,659,657,656,341,48,475,455,394,704,697,703,701,273,423,191,525,573,274,574,424,189,526,422,572,272,190,524,576,276,426,187,528,577,277,427,188,529,575,275,425,186,527,279,429,579,182,531,280,430,580,180,532,278,428,578,181,530,432,282,582,185,534,433,283,583,183,535,431,281,581,184,533,689,692,690,694,0,72,319,501,321,2,322,73,317,502,74,320,1,318,500,324,4,75,315,504,325,5,76,316,505,323,3,77,314,503,7,78,327,310,507,8,79,328,308,508,6,80,326,309,506,81,10,330,313,510,82,11,331,311,511,83,9,329,312,509,668,664,666,667,92,226,202,549,209,90,207,227,203,550,225,208,91,201,548,205,95,222,198,552,206,93,223,199,553,204,94,224,200,551,87,217,215,193,555,88,218,213,194,556,89,216,214,192,554,220,86,211,196,558,221,84,212,197,559,219,85,210,195,557,695,693,696,691,34,597,477,633,144,35,145,598,478,634,596,146,33,476,632,147,30,600,480,636,148,31,601,481,637,149,32,599,479,635,25,603,150,483,639,26,604,151,484,640,24,602,152,482,638,606,28,153,486,642,607,29,154,487,643,605,27,155,485,641,678,688,686,681,98,233,349,242,457,96,458,231,350,243,232,456,97,351,244,460,101,229,348,245,461,99,230,346,246,459,100,228,347,247,104,237,463,342,240,102,235,464,343,241,103,236,462,344,239,650,107,651,646,645,652,105,658,655,653,234,106,465,345,238,699,702,698,700,23,489,418,621,268,21,266,490,416,622,488,267,22,417,620,271,19,492,421,624,269,20,493,419,625,270,18,491,420,623,14,495,263,413,627,12,496,264,414,628,13,494,265,415,626,498,17,262,412,630,499,15,260,410,631,497,16,261,411,629,661,671,663,669,61,377,435,585,609,62,610,378,436,586,376,608,60,434,584,612,64,380,438,588,613,65,381,439,589,611,63,379,437,587,67,383,615,441,591,68,384,616,442,592,66,382,614,440,590,386,70,618,444,594,387,71,619,445,595,385,69,617,443,593,676,684,673,687 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#34588157c307db5531c4fa8d738de6f4f43dd6ced943a299dd02fbb5d9b36bf1, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 16:30:53 · history