Equation 677 Database

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Magma e98a30a98c28…

magma e98a30a98c28
Size
321
Isomorphism class hash
e98a30a98c28ace742aad80094cd7faf781b55994e8783a193cb9b979a6080d2
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 23:04:00
Display reorder
300,280,279,281,278,276,277,285,286,287,284,282,283,75,76,77,74,72,73,81,82,83,80,78,79,62,60,61,65,63,64,68,66,67,71,69,70,190,191,189,186,187,188,181,182,180,184,185,183,236,234,235,239,237,238,231,232,233,230,228,229,302,306,316,312,121,120,122,123,124,125,126,127,128,129,130,131,133,134,132,136,137,135,139,140,138,142,143,141,153,154,155,152,150,151,144,145,146,147,148,149,119,117,118,115,116,114,110,108,109,113,111,112,102,103,104,105,106,107,100,101,99,96,97,98,317,318,320,319,89,88,87,84,85,86,94,95,93,90,91,92,199,200,198,202,203,201,197,195,196,193,194,192,295,296,294,298,299,297,293,291,292,289,290,288,247,248,246,250,251,249,245,243,244,241,242,240,160,161,159,156,157,158,166,167,165,162,163,164,304,307,315,311,16,15,17,14,12,13,21,22,23,20,18,19,171,172,173,170,168,169,177,178,179,176,174,175,34,35,33,30,31,32,25,26,24,28,29,27,252,253,254,255,256,257,258,259,260,261,262,263,209,207,208,205,206,204,215,213,214,211,212,210,301,305,313,310,49,48,50,51,52,53,54,55,56,57,58,59,7,8,6,10,11,9,5,3,4,0,2,1,43,44,42,46,47,45,41,39,40,37,38,36,224,222,223,227,225,226,219,220,221,218,216,217,265,266,264,268,269,267,271,272,270,274,275,273,303,308,314,309 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#f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9, M = {61} 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 23:04:01 · history