Equation 677 Database

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Magma 981e7294bcf1…

magma 981e7294bcf1
Size
381
Isomorphism class hash
981e7294bcf13db1eec2b45d11bd976c95bd284b459c072059af6438be75d164
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:44:25
Display reorder
380,207,197,217,227,237,187,267,277,287,297,247,257,144,145,146,147,148,149,316,317,312,313,314,315,29,24,25,26,27,28,32,33,34,35,30,31,238,188,198,208,218,228,248,258,268,278,288,298,143,138,139,140,141,142,134,133,151,152,153,135,136,154,137,155,132,150,354,355,335,352,336,353,377,378,365,364,205,195,215,225,235,185,265,275,285,295,245,255,51,52,53,48,49,50,306,307,308,309,310,311,163,164,165,166,167,162,159,160,161,156,157,158,232,182,192,202,212,222,242,252,262,272,282,292,119,114,115,116,117,118,110,109,57,58,59,111,112,54,113,55,108,56,339,340,356,349,357,350,375,373,368,366,209,199,219,229,239,189,269,279,289,299,249,259,169,170,171,172,173,168,302,303,304,305,301,300,37,38,39,40,41,36,47,42,43,44,45,46,234,184,194,204,214,224,244,254,264,274,284,294,64,65,60,61,62,63,67,66,174,175,176,68,69,177,70,178,71,179,358,359,337,342,338,341,379,370,361,367,203,193,213,223,233,183,263,273,283,293,243,253,6,7,8,9,10,11,322,323,318,319,320,321,78,79,80,81,82,83,76,77,72,73,74,75,231,180,190,201,211,221,241,251,261,271,281,290,107,102,103,104,105,106,98,97,0,2,3,99,100,4,101,5,96,1,331,332,344,347,343,348,374,372,363,360,200,191,210,220,230,181,260,270,280,291,240,250,17,12,13,14,15,16,324,325,326,327,328,329,88,89,84,85,86,87,93,94,95,90,91,92,236,186,196,206,216,226,246,256,266,276,286,296,127,128,129,130,131,126,120,125,22,23,18,121,122,19,123,20,124,21,334,333,345,330,346,351,371,376,369,362 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#d9df7de9a291eb9f8afa3ed926081c844b8ee7df4e18920313d7d7d6494810a4, M = {76} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:44:26 · history