Equation 677 Database

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Magma d24a5928b26a…

magma d24a5928b26a
Size
595
Isomorphism class hash
d24a5928b26aef13eefa4208ebd6e0c92a5b0997e84f559a8e2d4679795c5931
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 23:50:27
Display reorder
24,27,25,26,29,28,86,85,87,82,83,84,67,66,68,63,64,65,396,398,397,401,399,400,339,341,340,338,336,337,538,513,569,561,560,245,244,174,241,242,243,159,77,78,79,80,81,31,30,32,33,34,35,43,42,44,190,191,154,182,181,183,151,13,12,137,136,138,139,140,220,169,222,223,224,221,168,178,177,176,150,179,180,381,383,382,378,379,380,491,490,489,488,486,487,483,485,484,480,482,481,410,409,408,412,413,411,493,492,494,495,496,497,457,458,456,461,459,460,292,291,293,288,289,290,354,356,355,358,359,357,549,550,520,533,532,527,535,536,563,555,557,584,567,552,586,593,54,53,55,56,51,52,18,23,19,20,21,22,73,72,74,75,70,71,120,125,121,122,123,124,108,107,109,110,105,106,96,95,97,98,94,208,218,167,219,216,217,166,233,237,171,234,235,236,503,502,501,500,498,499,427,426,428,430,431,429,280,279,281,278,276,277,507,506,505,504,509,508,322,321,323,318,319,320,272,271,270,274,275,273,302,301,300,304,305,303,314,313,312,315,316,317,523,524,514,548,551,530,519,511,562,573,578,582,587,591,585,565,102,101,103,104,99,100,10,9,11,6,7,8,1,0,2,3,4,5,57,62,58,59,60,61,47,46,48,49,50,45,146,145,147,148,149,257,250,247,251,248,249,232,256,255,246,252,253,254,455,454,453,452,450,451,434,433,432,437,435,436,423,425,424,421,422,420,464,462,463,466,467,465,446,445,444,448,449,447,345,347,346,344,342,343,472,471,473,468,469,470,443,442,441,438,439,440,541,534,525,518,522,512,526,521,553,558,559,594,554,556,590,572,90,89,91,92,93,88,76,202,203,200,158,201,192,155,193,156,194,195,210,209,162,111,112,113,142,141,143,144,230,231,173,175,239,240,172,238,153,188,189,186,187,152,225,229,226,170,227,228,388,387,389,385,386,384,350,349,348,353,351,352,392,391,390,394,393,395,403,402,404,405,406,407,286,285,287,282,283,284,331,330,332,333,334,335,308,307,306,310,311,309,327,329,328,325,326,324,547,545,529,515,539,516,510,540,581,589,574,592,564,588,571,570,114,119,115,116,117,118,69,198,199,157,196,197,205,160,206,204,161,207,215,214,165,128,129,127,15,14,16,17,184,185,212,211,163,213,164,126,38,37,39,40,41,36,134,133,135,130,131,132,415,414,416,418,419,417,479,475,478,474,476,477,265,264,266,269,267,268,295,294,296,297,298,299,369,371,370,368,366,367,261,263,262,260,259,258,375,377,376,374,372,373,362,361,360,363,364,365,528,537,543,546,544,531,517,542,566,575,580,579,568,583,576,577 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#3cc60f474fc5309f8bfdc916c4fdc0ad032cdecf3f770b83999110b499ecb4f1, M = the submagma generated by {6, 18} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-08 23:50:28 · history