Equation 677 Database

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Magma 15d9e71dbec2…

magma 15d9e71dbec2
Size
321
Isomorphism class hash
15d9e71dbec2b576e2fac4cf0ec265a500e997eceabcb9bf3f6c64a7fe6463fe
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 22:51:20
Display reorder
300,123,113,11,88,101,111,9,89,124,99,112,10,125,100,87,7,109,84,122,97,8,110,85,120,98,6,108,86,121,96,119,2,94,129,107,117,1,95,130,105,118,0,93,131,106,5,115,90,128,103,3,116,91,126,104,4,114,92,127,102,315,316,301,302,266,265,71,264,267,268,69,269,270,271,272,70,274,275,273,67,260,261,262,263,68,252,253,254,255,66,256,257,258,259,288,62,289,291,290,293,60,292,295,294,297,61,296,299,298,65,285,284,287,286,63,277,276,279,278,64,281,280,283,282,320,319,318,317,205,234,144,235,204,236,145,237,207,206,238,146,209,208,239,147,232,233,211,210,148,228,229,213,212,149,230,231,215,214,247,150,246,216,217,249,151,248,218,219,251,152,250,220,221,153,245,244,222,223,154,241,240,224,225,155,243,242,226,227,309,310,308,307,187,133,27,12,186,134,28,13,189,188,132,29,190,191,14,26,136,15,184,185,24,137,16,180,181,25,135,17,182,183,139,33,18,199,198,140,34,19,201,200,138,35,20,202,203,32,142,21,196,197,30,143,22,193,192,31,141,23,194,195,311,312,305,306,162,72,47,48,163,73,45,49,164,165,74,46,167,166,50,43,75,51,161,160,44,76,52,156,157,42,77,53,159,158,78,38,54,174,175,79,36,55,177,176,80,37,56,179,178,41,81,57,173,172,39,82,58,168,169,40,83,59,171,170,313,314,303,304 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#bc5f623c03e0cf031de7da5cba3786bb6161d1a009770b59759abcaaa846aef4, 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 22:51:21 · history