Equation 677 Database

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Magma 53f0588cd54b…

magma 53f0588cd54b
Size
321
Isomorphism class hash
53f0588cd54b674200528657d257e7eaf51008136b6b866647042bebbdd65b97
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 22:45:42
Display reorder
300,40,155,165,72,181,73,41,153,163,182,74,42,154,164,183,75,39,157,227,233,76,38,156,166,232,214,241,247,167,180,33,150,160,70,21,34,151,161,71,22,35,152,162,69,20,36,149,159,67,23,208,224,158,68,24,37,225,226,243,238,311,313,315,312,285,287,284,14,286,15,276,279,277,278,16,280,283,281,282,17,296,299,297,298,18,288,291,289,290,19,292,295,293,294,265,267,264,12,266,269,271,268,13,270,273,275,272,11,274,260,263,261,8,262,252,255,253,9,254,256,259,257,10,258,320,317,319,318,95,130,80,30,236,240,216,221,81,4,29,94,129,82,205,207,98,133,79,2,31,96,131,77,3,32,97,132,78,0,91,43,85,26,6,92,44,86,27,7,93,45,87,28,5,90,46,84,206,204,88,47,83,25,1,89,209,215,239,237,308,302,303,306,176,115,190,52,145,53,174,113,188,143,51,175,114,189,144,55,179,118,193,148,56,177,116,191,146,54,178,117,192,147,172,110,186,211,169,231,111,235,49,228,173,112,187,50,168,171,109,185,210,248,230,245,234,242,229,249,108,184,48,170,305,310,314,316,198,125,104,61,139,62,199,123,102,137,60,197,124,103,138,57,194,128,107,142,58,195,126,105,140,59,196,127,106,141,202,121,100,65,135,203,122,101,66,136,201,220,218,64,223,200,120,217,212,246,251,219,244,213,222,250,119,99,63,134,307,309,301,304 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#9741437d1171904ffa64043ea6d962aefa7dc37d5417f733d15a56c498f18cdb, 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 22:45:43 · history