Equation 677 Database

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Magma 95b31b054b88…

magma 95b31b054b88
Size
321
Isomorphism class hash
95b31b054b8819fa97440f59a1cd6903f51be8d110a714243ecbf8328e8efb16
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 22:49:03
Display reorder
300,218,99,123,88,65,216,121,89,66,97,217,98,122,90,64,95,214,119,91,68,96,215,120,92,69,94,213,118,93,67,129,250,248,86,63,127,222,103,87,61,128,223,104,85,62,220,125,101,82,59,221,126,102,83,60,219,124,100,84,58,301,309,313,316,273,272,52,275,274,265,53,266,267,264,269,268,54,270,271,257,256,55,259,258,261,260,56,262,263,253,252,57,254,255,50,296,297,299,298,51,288,289,290,291,49,292,293,295,294,280,46,281,282,283,285,47,284,286,287,276,48,277,278,279,319,317,318,320,150,135,12,241,73,148,13,239,74,133,149,134,14,240,75,131,153,15,237,72,132,151,16,238,70,130,152,17,236,71,18,145,141,247,79,19,146,139,245,80,20,147,140,246,81,144,21,137,243,78,142,22,138,244,76,143,23,136,242,77,311,308,304,303,198,35,0,32,206,199,2,33,204,36,200,34,1,31,205,38,197,4,28,202,39,195,5,29,203,37,196,3,30,201,7,251,41,249,212,8,190,42,105,210,6,191,40,24,211,192,10,44,26,208,193,11,45,27,209,194,9,43,25,207,314,307,315,302,162,229,106,183,175,160,107,181,176,227,161,228,108,182,177,225,165,109,179,174,226,163,110,180,172,224,164,111,178,173,112,157,235,189,166,113,158,233,187,167,114,159,234,188,168,156,115,231,185,169,154,116,232,186,170,155,117,230,184,171,306,312,305,310 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#a3dbb2a8d5932ce23601e140d077e70c3bff24b108fb14183b80120946e543a6, 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 22:49:04 · history