Equation 677 Database

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Magma 629362748b5a…

magma 629362748b5a
Size
321
Isomorphism class hash
629362748b5a5374bfe975388770a146476b354bbf2f706490144bbc18fa6964
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 22:37:25
Display reorder
300,158,144,19,55,134,156,145,56,20,132,157,146,18,54,133,147,161,22,58,137,148,159,23,59,135,149,160,21,57,136,164,150,25,61,129,162,151,26,62,130,163,152,24,60,131,153,167,28,64,128,154,165,29,65,126,155,166,27,63,127,305,310,303,307,262,261,215,263,260,253,252,254,213,255,257,256,214,258,259,272,273,211,274,275,265,264,212,266,267,268,269,210,270,271,284,285,206,286,287,276,277,204,278,279,280,281,205,282,283,297,296,209,298,299,289,288,207,290,291,293,292,208,294,295,319,317,320,318,140,194,77,39,14,138,192,40,75,12,139,193,76,41,13,197,143,73,38,17,195,141,74,36,15,196,142,72,37,16,239,200,68,30,237,230,198,66,31,231,235,199,67,32,233,203,251,71,33,249,201,243,69,34,240,202,247,70,35,245,301,309,315,314,109,218,81,47,116,110,216,45,82,114,108,217,83,46,115,221,112,80,43,119,219,113,78,44,117,220,111,79,42,118,107,224,87,53,122,105,222,88,51,120,106,223,89,52,121,227,103,86,49,125,225,104,84,50,123,226,102,85,48,124,312,308,304,302,182,172,6,95,99,180,173,93,7,100,181,171,8,94,101,168,185,9,91,98,169,183,10,92,96,170,184,11,90,97,188,178,4,238,236,186,179,5,228,229,187,177,3,232,234,174,191,1,248,250,175,189,0,241,242,176,190,2,244,246,306,313,316,311 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#6da5e6765bc0adc27e9eb05052cc3d9b74fd6a5fdc541eafc0e7aaffee5eac36, 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 22:37:26 · history