Equation 677 Database

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Magma 67ea625d203d…

magma 67ea625d203d
Size
321
Isomorphism class hash
67ea625d203d75f5edae100546670a788a7f2ebdf8ddd1cf2490e26673f7b3fe
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 22:44:59
Display reorder
300,54,224,109,237,70,55,71,222,110,238,223,69,56,108,239,66,57,227,112,236,67,58,225,113,234,68,59,226,111,235,61,219,52,115,228,62,220,53,116,229,60,221,51,114,230,218,64,48,118,231,119,216,65,49,232,217,63,50,117,233,313,315,308,309,290,291,289,288,246,294,247,295,293,292,299,248,298,297,296,249,286,287,284,285,250,278,279,277,276,251,282,283,281,280,244,255,254,252,253,245,259,258,256,257,243,263,262,261,260,267,240,266,264,265,268,271,241,270,269,275,242,274,272,273,318,319,317,320,33,80,21,189,130,34,131,78,22,190,79,129,35,23,191,126,32,83,20,188,127,30,81,18,186,128,31,82,19,187,121,75,24,12,180,122,76,25,13,181,120,77,26,14,182,74,124,27,15,183,16,72,125,28,184,73,123,29,17,185,311,301,302,316,201,136,212,165,85,202,86,137,210,166,135,84,203,211,167,88,200,132,215,164,89,198,133,213,162,87,199,134,214,163,91,142,192,207,156,92,143,193,208,157,90,141,194,209,158,138,94,195,206,159,204,139,95,196,160,140,93,197,205,161,314,305,310,307,40,177,97,153,10,41,11,178,98,154,179,9,39,96,155,6,36,176,100,152,7,37,174,101,150,8,38,175,99,151,0,168,46,103,144,2,169,47,104,145,1,170,45,102,146,171,4,42,106,147,107,172,5,43,148,173,3,44,105,149,312,304,306,303 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#8819209ab5a908e1474d8d2e3196687ec1a856ed03900dcfe11c102e06a1cf49, 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 22:45:00 · history