Equation 677 Database

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Magma 731c61e3acf3…

magma 731c61e3acf3
Size
321
Isomorphism class hash
731c61e3acf3d36ff0f1936a13dcdd3065e26d8020f3340f6612d28adbaf5c80
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 22:55:46
Display reorder
300,108,9,74,96,119,10,75,97,109,120,76,11,98,110,121,12,73,95,107,118,13,72,94,105,116,14,226,228,106,117,7,80,102,113,124,8,81,103,114,125,6,82,104,115,126,79,1,101,112,123,77,4,99,111,122,78,5,100,229,230,315,304,312,301,259,246,258,257,256,247,261,260,262,263,253,248,252,254,255,249,269,268,270,271,250,273,272,274,275,251,264,265,266,267,244,281,280,282,283,245,285,284,286,287,243,277,276,278,279,293,240,292,294,295,297,241,296,298,299,288,242,289,290,291,320,317,319,318,2,84,66,135,231,227,67,133,140,141,68,83,134,3,139,87,69,138,145,144,85,70,136,147,146,86,71,137,143,142,90,64,130,150,151,88,65,131,153,152,89,63,132,148,149,60,93,129,154,155,61,91,127,156,157,62,92,128,232,233,309,308,302,303,55,18,159,204,193,19,160,205,56,194,158,20,203,54,192,17,162,207,58,196,15,163,208,59,197,16,161,206,57,195,24,165,210,53,199,25,166,211,51,200,26,164,209,52,198,168,23,213,225,202,234,21,237,50,236,167,22,212,0,201,305,313,310,316,173,31,218,40,182,32,219,41,174,183,217,30,39,172,181,27,214,43,169,185,28,215,44,170,186,29,216,42,171,184,37,222,46,179,188,38,223,47,180,189,36,221,45,178,187,220,33,49,175,235,239,34,224,176,191,238,35,48,177,190,306,311,307,314 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#d368fcffc98defb742f81d5388b25ae4c38c7de7079297526f4ed93fca5d0bec, 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 22:55:47 · history