Equation 677 Database

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Magma e4697ec970e2…

magma e4697ec970e2
Size
321
Isomorphism class hash
e4697ec970e23e7df423e6acb0b24bb89d57cb36beca7c6aca1e089324b11d2a
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 22:36:58
Display reorder
316,252,249,275,261,90,66,134,223,91,67,135,222,92,64,220,136,93,65,221,137,253,248,262,274,72,88,216,132,70,89,133,217,71,87,131,215,69,85,219,129,250,251,260,273,68,86,130,218,104,105,106,107,108,109,110,111,285,283,284,282,304,300,305,318,277,294,280,293,23,205,182,97,24,206,183,98,25,209,96,181,26,207,94,179,27,208,180,95,211,18,102,174,295,276,292,281,210,19,175,103,214,20,101,176,212,21,177,99,213,22,178,100,194,195,193,197,198,196,200,201,202,203,204,199,310,306,302,313,191,16,1,127,192,17,128,0,272,237,259,232,190,14,2,126,271,236,233,258,189,15,125,3,10,184,4,120,11,185,121,5,9,186,122,6,235,270,234,257,13,187,123,7,12,188,124,8,148,146,147,151,149,150,153,152,290,291,289,288,303,319,308,312,279,287,286,278,56,142,48,113,57,143,49,112,245,265,254,242,58,144,115,50,59,145,51,114,140,60,117,53,264,246,243,255,141,61,52,116,139,62,118,55,138,63,54,119,263,247,244,256,77,78,76,73,74,75,83,84,81,79,80,82,307,301,309,311,43,164,37,163,44,165,161,35,42,166,162,36,46,167,33,159,47,168,34,160,45,169,158,32,268,241,239,267,269,240,266,238,170,41,154,28,171,39,31,157,172,40,155,29,173,38,156,30,224,225,226,227,228,229,230,231,298,296,297,299,314,317,315,320 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#65891b0f2ef20500afb660f1d25606412fdc1bf33a195bdba8e3c07ff4e9e9d9, 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 22:36:59 · history