Equation 677 Database

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Magma 01598adf0a19…

magma 01598adf0a19
Size
321
Isomorphism class hash
01598adf0a196924b502f83309f4db085115d1e299cfa84522dc432cd19e4e3f
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:55:28
Display reorder
300,108,47,130,112,120,131,109,113,121,46,132,178,182,114,119,129,199,194,115,123,127,215,210,116,124,128,231,226,117,122,53,110,118,136,125,152,51,111,137,126,155,52,191,138,183,49,150,200,135,201,50,151,216,133,217,134,48,149,232,233,305,301,306,308,264,247,265,267,266,269,268,271,270,248,272,246,273,275,274,260,261,250,263,262,252,253,251,255,254,256,257,249,259,258,245,288,290,289,291,292,243,294,293,295,297,244,298,296,299,241,285,287,284,286,242,276,279,277,278,281,240,280,283,282,319,317,320,318,24,61,219,167,238,235,22,168,206,62,203,60,23,169,222,148,20,64,166,173,147,21,65,164,189,185,19,63,165,172,59,15,170,141,174,13,57,171,142,175,14,58,188,143,190,55,18,205,144,207,56,16,221,145,223,146,54,17,237,239,315,312,304,303,28,38,159,11,68,160,29,12,66,39,161,37,30,10,67,158,27,41,7,71,156,25,42,8,69,157,26,40,9,70,44,34,139,187,73,35,176,184,162,179,36,43,140,163,72,209,33,218,236,211,225,31,234,204,227,220,192,32,202,195,302,307,310,313,76,1,101,87,97,102,74,88,98,0,100,2,75,86,99,104,79,3,90,96,105,77,4,91,94,103,78,5,89,95,6,82,93,106,186,80,177,180,107,153,81,45,92,181,154,208,85,212,198,229,224,83,228,214,197,230,193,84,196,213,309,316,314,311 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*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, 5, B) with E = magma#cc21ed90a723dc84f76676d15ec858e33ef625916c28841b110b43408fa38d16, M = {60} 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, 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: 21.

last edited by qawbecrdtey at 2026-10-01 22:55:29 · history