Equation 677 Database

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Magma 14a1c5a4677d…

magma 14a1c5a4677d
Size
321
Isomorphism class hash
14a1c5a4677d7cd04d8e224585172b03ea64d4c0864011b586d073f9c8a6bf8d
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 22:31:49
Display reorder
300,116,57,24,240,241,117,55,22,244,245,118,56,23,248,249,60,119,20,237,236,58,120,21,109,1,59,121,19,232,233,30,114,63,107,4,28,115,61,108,5,29,113,62,106,6,110,26,66,103,3,111,27,64,104,0,112,25,65,105,2,314,316,307,306,291,33,290,288,289,294,31,295,292,293,299,32,298,296,297,36,286,287,285,284,34,278,279,276,277,35,282,283,281,280,255,254,39,252,253,259,258,37,256,257,263,262,38,260,261,266,267,42,264,265,270,271,40,268,269,274,275,41,273,272,319,317,318,320,229,67,193,180,125,230,68,194,178,126,231,69,195,179,127,70,228,192,183,124,71,226,190,181,122,72,227,191,182,123,184,220,73,175,131,185,221,74,176,132,186,222,75,177,133,223,187,76,174,130,224,188,77,172,128,225,189,78,173,129,302,301,311,308,157,10,242,139,243,158,11,246,137,247,156,12,250,138,251,9,153,238,135,239,7,154,146,136,165,8,155,234,134,235,150,163,16,145,167,151,164,17,143,168,152,162,18,144,166,159,149,15,141,170,160,147,13,142,171,161,148,14,140,169,305,313,303,315,204,87,43,98,217,202,85,44,99,218,203,86,45,97,219,90,207,46,101,216,88,205,47,102,214,89,206,48,100,215,49,199,82,96,208,50,200,83,94,209,51,201,84,95,210,198,52,81,92,211,196,53,79,93,212,197,54,80,91,213,304,310,309,312 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#4dbd6b0006d3996c22611f6a9a74b6d8666415e8467cb95ff3380ed5b17e9234, 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 22:31:50 · history