Equation 677 Database

← all  ·  ← by size  ·  ← size 595

Magma 335705028f35…

magma 335705028f35
Size
595
Isomorphism class hash
335705028f357f01d109a9c97a1e7ba9933005c025f4c3ff4a6a9ac28053e770
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
2026-10-07 23:45:31
Display reorder
163,162,165,166,164,161,116,118,117,113,114,115,73,72,71,74,75,76,404,403,405,406,407,402,394,393,395,390,391,392,521,528,536,562,573,172,171,170,167,168,169,110,112,111,109,107,108,146,145,144,149,147,148,32,34,33,29,30,31,191,187,195,183,256,253,199,201,200,196,197,198,238,249,239,242,240,241,2,4,3,1,119,0,478,477,479,474,475,476,419,418,414,415,416,417,439,438,440,441,442,443,433,432,434,435,436,437,389,388,384,385,386,387,396,401,397,398,399,400,429,428,430,431,426,427,470,469,471,472,473,468,534,529,544,514,527,537,551,543,584,563,572,574,575,571,593,583,211,213,212,209,210,208,235,237,236,234,232,233,251,255,182,188,192,184,46,45,44,43,41,42,103,102,101,104,105,106,125,124,123,122,120,121,81,80,82,77,78,79,221,220,222,224,225,223,463,462,464,465,466,467,423,422,424,425,420,421,383,382,378,379,380,381,504,509,505,506,507,508,411,410,412,413,408,409,493,492,494,495,496,497,265,264,266,267,268,269,303,302,304,305,300,301,542,548,530,516,550,546,522,526,586,581,567,591,579,560,589,564,21,20,22,19,17,18,137,136,135,133,134,132,38,40,39,35,36,37,142,141,143,139,140,138,60,59,61,64,62,63,98,100,99,95,96,97,24,23,25,26,27,28,156,158,157,159,179,160,364,363,365,360,361,362,501,500,502,503,498,499,461,460,456,457,458,459,270,275,271,272,273,274,485,484,480,481,482,483,332,331,333,334,335,330,339,338,340,341,336,337,342,347,343,344,345,346,515,539,525,533,532,512,513,519,594,570,588,569,557,556,578,555,204,203,202,205,206,207,226,228,227,231,229,230,252,257,181,190,194,186,83,85,84,86,87,88,90,89,91,94,92,93,53,55,54,56,57,58,154,153,155,150,151,152,177,176,178,174,175,173,352,351,353,348,349,350,314,313,315,316,317,312,453,452,454,455,450,451,306,311,307,308,309,310,295,294,296,297,298,299,279,278,280,281,276,277,323,322,318,319,320,321,263,262,259,258,260,261,541,538,518,523,549,545,535,524,592,558,585,561,568,565,566,582,6,5,7,10,8,9,131,130,129,127,128,126,12,11,13,15,16,14,47,49,48,50,51,52,189,185,193,180,254,250,218,217,219,215,216,214,245,244,243,247,248,246,67,66,65,70,68,69,293,292,288,289,290,291,448,447,449,444,445,446,490,489,491,486,487,488,356,355,357,358,359,354,286,285,287,282,283,284,324,329,325,326,327,328,370,369,371,366,367,368,375,374,376,377,372,373,511,520,547,517,531,510,552,540,553,554,576,559,587,580,577,590 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#53d992532d406ee1a16d046074f6b11dc06c8f5c6df8c27dc9277719dd794878, M = the submagma generated by {0, 24} (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 2026-10-07 23:45:32 · history