Equation 677 Database

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Magma 9b3ce7f51470…

magma 9b3ce7f51470
Size
321
Isomorphism class hash
9b3ce7f5147062338f872535f088d61a6d026d2ded1e0369ff08386fdbcaab71
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 23:04:08
Display reorder
300,137,136,135,132,133,134,142,143,141,138,139,140,214,215,213,210,211,212,205,206,204,208,209,207,273,274,275,272,270,271,264,265,266,267,268,269,1,0,2,3,4,5,6,7,8,9,10,11,122,120,121,125,123,124,128,126,127,131,129,130,301,309,312,314,44,43,42,46,47,45,41,39,40,37,38,36,81,82,83,80,78,79,72,73,74,75,76,77,91,92,90,94,95,93,89,87,88,85,86,84,70,71,69,66,67,68,61,62,60,64,65,63,58,59,57,54,55,56,49,50,48,52,53,51,317,318,319,320,165,167,166,163,164,162,158,156,157,161,159,160,282,283,284,285,286,287,280,281,279,276,277,278,169,170,168,172,173,171,175,176,174,178,179,177,226,227,225,222,223,224,217,218,216,220,221,219,145,146,144,148,149,147,151,152,150,154,155,153,304,305,310,313,294,296,295,299,297,298,291,292,293,290,288,289,237,238,239,236,234,235,228,229,230,231,232,233,107,105,106,103,104,102,98,96,97,101,99,100,184,185,183,180,181,182,190,191,189,186,187,188,244,245,243,240,241,242,250,251,249,246,247,248,303,311,306,316,110,109,108,112,113,111,115,116,114,118,119,117,254,252,253,257,255,256,260,258,259,263,261,262,31,32,30,34,35,33,29,27,28,25,26,24,22,23,21,18,19,20,13,14,12,16,17,15,201,202,203,200,198,199,192,193,194,195,196,197,302,308,307,315 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 = {63} 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 23:04:09 · history