Equation 677 Database

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Magma 0821a9c9a873…

magma 0821a9c9a873
Size
321
Isomorphism class hash
0821a9c9a8738e244beadf7673e4f0d4cb1bbba7264fd5edc69103e67eabb8b0
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 22:51:09
Display reorder
300,15,69,188,181,4,16,5,70,186,182,17,3,71,187,180,72,14,1,191,184,73,12,0,189,185,74,13,2,190,183,21,10,67,251,250,11,68,192,22,179,66,9,247,23,246,6,63,195,20,177,7,64,193,18,178,8,65,194,19,176,313,315,308,303,40,273,275,274,272,41,265,264,266,267,39,269,268,270,271,256,43,257,259,258,260,44,261,262,263,252,42,253,254,255,46,296,297,299,298,289,288,290,47,291,292,293,295,45,294,280,281,282,49,283,284,285,286,50,287,277,276,278,48,279,319,318,317,320,80,213,237,169,202,78,203,211,235,167,79,204,212,236,168,209,76,205,233,165,210,77,206,234,166,208,75,207,232,164,86,200,219,243,175,201,217,241,84,173,218,199,242,85,174,196,215,239,82,171,197,216,240,83,172,198,214,238,81,170,311,305,307,306,89,140,146,128,157,87,155,138,147,126,88,156,139,148,127,136,92,153,149,124,137,90,154,150,125,135,91,152,151,123,95,163,248,249,134,161,144,145,93,132,244,162,245,94,133,159,142,36,98,130,160,143,37,96,131,158,141,38,97,129,314,301,316,304,26,101,56,122,225,24,223,99,54,120,25,224,100,55,121,104,29,221,52,118,102,27,222,53,119,103,28,220,51,117,32,231,107,62,113,229,105,60,30,111,106,230,61,31,112,227,110,58,35,116,228,108,59,33,114,226,109,57,34,115,302,312,309,310 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#b9c83ee29c9828886a1d9280722af908f3a23a39dfe3e8d4571f7572270a5310, 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 22:51:09 · history