Equation 677 Database

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Magma 3c0dd5c3b4db…

magma 3c0dd5c3b4db
Size
321
Isomorphism class hash
3c0dd5c3b4db0aa37d946781111a4f06009e35edeb35fb1bde2e7a09f1d5fdc1
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 22:21:27
Display reorder
300,34,61,77,99,44,35,59,75,100,45,60,98,33,76,43,31,57,73,102,41,32,58,74,103,230,223,226,228,101,42,53,39,82,97,47,51,40,80,95,48,52,38,81,96,46,56,36,78,93,49,54,37,79,94,50,55,224,229,231,225,315,304,303,316,280,129,282,281,283,284,130,286,285,287,131,276,277,279,278,292,128,294,293,295,296,126,298,297,299,289,127,291,288,290,135,272,274,273,275,136,265,267,264,266,137,269,271,268,270,134,256,258,257,259,132,260,262,261,263,133,252,254,253,255,320,317,318,319,155,116,170,68,221,236,233,238,69,10,115,67,154,169,0,157,118,172,71,1,158,119,173,72,3,156,117,171,70,4,121,153,168,66,5,122,151,166,64,6,120,152,167,65,7,124,149,164,62,8,125,150,165,63,9,123,235,237,227,220,311,314,310,301,179,2,110,195,193,180,191,111,188,88,27,189,181,109,89,182,28,113,186,90,183,29,114,187,91,184,30,112,185,92,208,177,108,219,217,214,178,106,207,205,203,176,107,213,211,196,174,105,251,249,246,239,232,245,243,240,175,104,201,199,306,307,302,305,144,87,13,194,190,145,192,11,160,25,86,159,143,12,26,147,84,16,162,23,148,85,14,163,24,146,83,15,161,22,210,142,19,218,215,216,140,17,206,202,204,141,18,212,209,198,139,21,250,247,248,234,222,244,241,242,138,20,200,197,309,312,308,313 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#0d8cdfdeb3c53efefcd572d9bf5ad220efd26f91f8a2b4cfd66b53f1dccf6eeb, 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 22:21:28 · history