Equation 677 Database

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Magma fceda59b47d0…

magma fceda59b47d0
Size
321
Isomorphism class hash
fceda59b47d01405f28fdeed89fd1130bde0b980c3acb5df8ab73022c2234f4b
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 22:33:14
Display reorder
300,94,101,184,112,148,95,99,146,182,113,93,100,147,183,114,97,104,144,180,111,98,102,145,181,109,96,103,143,179,110,188,92,107,154,116,90,105,152,186,117,91,106,153,187,118,238,237,150,240,239,247,246,151,249,248,108,12,149,185,115,310,316,315,312,259,257,258,256,165,263,261,166,262,260,255,253,164,254,252,271,269,161,270,268,275,272,162,274,273,267,265,163,266,264,282,283,281,156,280,287,285,157,286,284,279,276,155,278,277,292,295,159,294,293,297,299,160,298,296,288,291,158,290,289,319,318,317,320,68,47,120,138,0,69,48,2,121,139,67,46,1,119,137,71,43,4,123,141,72,44,5,124,142,70,45,3,122,140,126,74,53,7,136,75,54,8,127,134,73,52,6,125,135,49,77,10,129,132,50,78,11,130,133,51,76,9,128,131,304,301,303,302,84,31,203,37,16,82,32,17,204,38,83,33,18,202,39,80,30,15,206,40,81,28,13,207,41,79,29,14,205,42,209,88,25,22,35,86,26,23,210,36,87,27,24,208,34,243,242,21,241,236,250,244,19,251,245,189,85,20,211,89,314,311,309,313,214,191,215,168,56,216,192,57,217,169,212,190,55,213,167,220,194,59,221,171,223,195,60,222,172,218,193,58,219,170,226,227,197,62,174,229,198,63,228,175,224,196,61,225,173,200,233,65,232,177,201,235,66,234,178,199,230,64,231,176,308,305,306,307 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#5c1fa523b4d9d2fbb415708ccaff34546079d57eeb66e712dcba93d7172179c8, 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 22:33:15 · history