Equation 677 Database

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Magma d06c56dc733c…

magma d06c56dc733c
Size
321
Isomorphism class hash
d06c56dc733cfc34a6ba50daf8f8dd2f5a64934068c8b09208876f4f45bcf4fd
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 22:49:21
Display reorder
300,40,181,152,54,194,153,41,52,195,182,151,183,42,53,193,184,154,43,57,191,185,155,44,55,239,237,234,220,56,192,60,179,38,150,187,180,39,148,58,188,178,37,149,59,186,34,176,146,62,189,35,177,147,61,190,36,236,233,222,238,311,314,313,309,4,280,283,281,282,286,5,285,287,284,278,277,3,276,279,292,295,7,293,294,296,299,8,297,298,289,290,6,288,291,273,272,10,275,274,265,11,266,264,267,269,9,270,268,271,13,256,259,257,258,14,260,262,261,263,12,252,254,253,255,317,320,318,319,15,123,63,109,230,223,221,228,128,124,64,122,45,110,129,119,65,18,111,127,120,66,16,112,125,121,67,17,113,126,107,115,49,68,132,116,50,69,108,133,114,51,70,106,134,48,117,71,104,131,46,118,72,105,130,47,229,224,227,231,303,305,301,304,23,103,141,77,200,142,24,78,201,101,140,102,22,76,199,99,144,19,80,203,100,145,20,81,204,98,143,21,79,202,218,95,27,139,217,93,214,137,74,197,94,26,138,73,198,25,97,136,248,250,247,226,232,242,244,241,96,135,75,196,316,312,315,310,28,88,167,210,160,165,29,208,161,89,166,87,30,209,159,91,170,31,206,156,92,168,32,207,157,90,169,33,205,158,219,86,1,173,216,84,215,171,212,164,85,2,172,213,163,0,83,175,251,249,246,225,235,245,243,240,82,174,211,162,307,306,308,302 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#a96a88e4cf05ff772a659e73be5ebad0179d3b86aa5fbe0be371d7ceb3ac096d, 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 22:49:22 · history