Equation 677 Database

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Magma 9f798dc48905…

magma 9f798dc48905
Size
321
Isomorphism class hash
9f798dc4890550fafc44710a4be649af98ab1b6a10f0397237add9e75fc039bb
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 23:00:08
Display reorder
300,238,37,156,135,239,157,38,230,133,231,234,158,134,36,235,159,148,40,131,175,160,227,41,132,226,161,149,39,130,174,155,126,162,43,170,153,124,163,44,168,154,125,164,42,169,129,151,165,46,173,127,152,166,47,171,128,150,167,45,172,306,305,315,313,299,240,296,298,297,288,241,290,291,289,294,292,295,242,293,280,283,243,282,281,284,287,244,286,285,276,278,245,279,277,263,262,260,246,261,254,255,252,247,253,259,258,256,248,257,274,275,273,249,272,266,267,265,250,264,271,270,269,251,268,320,319,317,318,211,144,59,188,223,57,142,209,189,221,210,58,190,143,222,55,207,147,191,219,56,208,145,192,220,54,206,146,193,218,202,194,50,139,214,200,195,48,140,212,201,196,49,141,213,197,205,53,138,217,198,203,51,136,215,199,204,52,137,216,304,303,311,309,187,13,60,236,237,61,14,185,229,228,186,62,232,12,233,63,183,16,103,105,64,184,17,224,225,65,182,15,102,104,178,101,66,19,108,176,99,67,20,106,177,100,68,18,107,97,181,69,22,111,98,179,70,23,109,96,180,71,21,110,316,302,314,307,86,112,25,80,0,26,113,84,78,2,85,24,79,114,1,28,89,115,83,4,29,87,116,81,5,27,88,117,82,3,92,75,31,118,7,90,76,32,119,8,91,77,30,120,6,74,95,34,121,10,72,93,35,122,11,73,94,33,123,9,308,301,310,312 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#eb741fb6db55479c3e56ca4f84f09a48d9f1cbf15ed347cc0747015cb842acab, 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 23:00:09 · history