Equation 677 Database

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Magma c392d1a54120…

magma c392d1a54120
Size
321
Isomorphism class hash
c392d1a54120eaac8f7a7ee32cfff9b18025ece949acb1a7cc808ea326dffba0
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 22:36:54
Display reorder
300,169,62,118,79,102,170,80,60,119,103,171,78,61,117,104,82,168,65,114,105,83,166,63,115,106,81,167,64,116,107,68,160,109,77,100,66,161,110,75,101,67,162,108,76,99,163,71,112,73,96,69,164,113,74,97,165,70,111,72,98,302,305,311,307,258,259,257,10,256,261,11,262,260,263,253,9,254,252,255,6,269,270,268,271,7,273,274,272,275,8,265,266,264,267,282,280,281,0,283,286,284,285,2,287,278,276,277,1,279,292,294,293,4,295,298,296,297,5,299,288,290,289,3,291,318,319,317,320,174,155,13,32,130,175,30,156,14,131,173,31,154,12,129,35,177,158,16,126,33,178,159,17,127,34,176,157,15,128,153,172,19,27,121,237,239,20,28,122,152,179,18,29,120,246,245,22,26,124,249,250,23,24,125,242,240,21,25,123,304,301,314,315,225,208,143,45,213,226,46,206,141,214,224,47,207,142,212,44,228,211,139,216,42,229,209,140,217,43,227,210,138,215,203,231,134,36,219,204,232,132,37,220,205,230,133,38,218,234,202,137,39,222,200,235,135,40,223,233,201,136,41,221,310,308,306,312,189,148,184,84,49,190,85,149,182,50,188,86,147,183,48,87,192,144,187,52,88,193,145,185,53,89,191,146,186,51,151,195,180,90,55,236,196,238,91,56,150,194,181,92,54,198,244,247,93,58,248,199,251,94,59,197,241,243,95,57,303,316,313,309 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#62fadf6abad0ff7e327687381d1d05b120aac2dcda3d9647c53ea471472f147e, 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 22:36:55 · history