Equation 677 Database

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Magma cc40ad2451c4…

magma cc40ad2451c4
Size
321
Isomorphism class hash
cc40ad2451c4da616b89f10288979803fdef897167d3f1e6da1436b690c3ed3d
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 22:45:18
Display reorder
300,73,243,87,37,171,38,74,244,88,172,245,36,72,89,173,40,76,242,86,170,41,77,240,84,168,39,75,241,85,169,79,249,93,43,177,80,250,94,44,178,78,251,95,42,179,82,248,92,46,176,83,246,90,47,174,81,247,91,45,175,313,307,311,305,264,265,267,15,266,16,268,269,271,270,272,17,273,275,274,14,260,261,263,262,12,252,253,255,254,13,256,257,259,258,288,289,290,21,291,293,292,294,22,295,297,296,299,23,298,285,284,286,20,287,276,277,278,18,279,281,280,282,19,283,320,318,319,317,102,148,136,27,161,28,103,149,137,159,147,29,104,135,160,26,105,144,132,157,24,106,145,133,158,25,107,146,134,156,100,154,142,33,167,101,155,143,34,165,99,153,141,35,166,96,150,138,32,163,97,151,139,30,164,98,152,140,31,162,316,306,310,308,8,114,183,48,65,49,6,115,184,63,116,50,7,185,64,51,11,117,182,61,52,9,118,180,62,53,10,119,181,60,3,112,189,54,71,4,113,190,55,69,5,111,191,56,70,2,108,188,57,67,1,109,186,58,68,0,110,187,59,66,315,302,309,301,218,201,229,131,215,129,216,202,230,213,203,130,217,228,214,127,221,200,232,211,128,219,198,233,212,126,220,199,231,210,224,192,235,122,206,222,193,236,120,204,223,194,234,121,205,227,195,238,125,209,225,196,239,123,207,226,197,237,124,208,314,303,312,304 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#90fd68087a2f09648803d65723dcc8788b62f036d4e0ed1478893fb37d6a20cd, 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 22:45:19 · history