Equation 677 Database

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Magma 552b6a8a71a5…

magma 552b6a8a71a5
Size
321
Isomorphism class hash
552b6a8a71a579393cb2d92a61c19fa8b434e3b45b2f6d50559fcfae97251145
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 22:38:07
Display reorder
300,62,16,194,148,117,17,149,60,192,118,15,147,61,193,119,12,65,197,144,116,13,63,195,145,114,14,64,196,146,115,68,200,22,154,108,66,198,23,155,109,67,199,21,153,110,203,71,18,150,111,201,69,19,151,112,202,70,20,152,113,302,304,301,307,251,268,269,271,270,272,275,249,273,274,265,266,250,264,267,253,247,252,255,254,257,248,256,259,258,261,246,260,262,263,242,292,293,295,294,240,296,297,298,299,241,289,288,290,291,276,245,277,279,278,280,243,281,283,282,284,244,285,287,286,319,318,320,317,73,208,4,225,224,209,226,74,5,227,207,223,72,3,222,204,76,1,216,217,205,77,0,218,219,206,75,2,220,221,79,10,214,236,237,80,11,215,238,239,78,9,213,235,234,6,82,210,229,228,7,83,211,230,231,8,81,212,232,233,312,311,313,314,40,184,91,174,160,185,175,41,92,161,183,176,39,90,159,180,36,94,177,156,181,37,95,178,157,182,38,93,179,158,46,89,190,172,166,47,87,191,173,167,45,88,189,171,165,85,42,186,168,162,86,43,187,169,163,84,44,188,170,164,305,303,308,310,26,102,129,133,50,103,134,28,130,48,104,132,25,131,49,105,33,128,136,53,106,35,126,137,51,107,31,127,135,52,29,120,100,139,56,24,121,101,140,54,27,122,99,138,55,123,34,96,142,59,124,30,97,143,57,125,32,98,141,58,306,315,316,309 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#7eb365a46a73bc671c535e7eab37a7fd590c6d5c6b4c14d45f700003c9150a2d, 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 22:38:08 · history