Equation 677 Database

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Magma c9c31874f409…

magma c9c31874f409
Size
321
Isomorphism class hash
c9c31874f4098120e771bccc0d62efdb18884a38165bf455040958e261847448
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 22:27:25
Display reorder
300,100,61,152,44,180,98,62,153,45,181,99,63,154,43,182,64,96,155,208,234,65,97,156,41,248,239,214,228,42,183,94,66,150,49,178,92,67,151,50,179,93,68,149,48,177,69,95,147,46,175,212,213,148,47,176,70,243,245,209,233,311,313,315,308,9,277,276,279,278,10,280,281,283,282,11,284,285,287,286,289,8,288,291,290,292,6,293,295,294,296,7,297,299,298,1,268,269,271,270,0,272,273,275,274,2,265,264,267,266,253,3,252,255,254,257,4,256,259,258,261,5,260,263,262,317,318,319,320,36,115,80,54,217,207,244,241,55,105,37,116,79,56,218,219,38,76,53,106,117,39,77,51,107,118,40,78,52,108,34,113,72,58,103,35,114,73,59,104,33,112,71,60,102,109,31,74,211,215,110,32,75,57,101,111,238,240,210,216,310,303,304,314,24,188,141,160,169,22,189,142,161,170,23,190,143,162,171,191,20,144,163,172,192,21,145,164,173,193,19,146,165,174,27,186,140,230,168,204,187,227,159,232,26,185,139,158,167,184,18,137,229,247,235,236,226,246,231,249,25,138,157,166,309,312,316,307,82,131,122,199,17,83,132,123,197,15,81,133,124,198,16,134,85,125,195,13,135,86,126,196,14,136,84,127,194,12,88,129,120,203,29,89,130,121,201,30,87,225,222,202,206,128,91,220,251,205,223,242,221,250,237,224,90,119,200,28,301,302,306,305 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#357eb5a07f294d712e4efb5d2eb529ba387854e51bbe679ac1cbb62e1e3b2fae, 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 22:27:26 · history